Tengo una sola actividad (MainActivity) que extiende la acción y la actividad e implementa NavigationDrawer. He configurado el drawertoggle en la actividad misma.

Estoy creando nuevos fragmentos a partir de un fragmento creado por otro fragmento creado a su vez por MainActivity. (MainActivity -> HomeFragment -> AnotherFragment).

MainActivity.java

public class MainActivity extends ActionBarActivity implements FragmentDrawer.FragmentDrawerListener, TitleSetter, NavigationDrawerEnabler{
    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);
        myToolbar = (Toolbar) findViewById(R.id.toolbar);
        setSupportActionBar(myToolbar);
        getSupportActionBar().setHomeButtonEnabled(true);
        //getSupportActionBar().setDisplayHomeAsUpEnabled(true);
        drawerFragment = (FragmentDrawer)
                getSupportFragmentManager().findFragmentById(R.id.fragment_navigation_drawer);
        setUp(R.id.fragment_navigation_drawer, (DrawerLayout) findViewById(R.id.drawer_layout), myToolbar);
        mDrawerLayout = (DrawerLayout) findViewById(R.id.drawer_layout);
        drawerFragment.setDrawerListener(this);
        // display the first navigation drawer view on app launch
        displayView(0);

    }


    @Override
    public boolean onCreateOptionsMenu(Menu menu) {
        // Inflate the menu; this adds items to the action bar if it is present.
        getMenuInflater().inflate(R.menu.menu_main, menu);
        return super.OncreateOptionsMenu(menu);
    }

    @Override
    public boolean onOptionsItemSelected(MenuItem item) {
        // Handle action bar item clicks here. The action bar will
        // automatically handle clicks on the Home/Up button, so long
        // as you specify a parent activity in AndroidManifest.xml.


        /*  This function is never called even if the Up caret button is pressed!!   */
     if (mDrawerToggle.isDrawerIndicatorEnabled() &&
                mDrawerToggle.onOptionsItemSelected(item))
            return true;
        switch (item.getItemId()) {
            case android.R.id.home:
                /*This case doesn't occur*/
                return true;
            case R.id.action_settings:
                return true;
            default:
                return super.onOptionsItemSelected(item);
        }
    }

    @Override
    public void onDrawerItemSelected(View view, int position) {
        mDrawerLayout.closeDrawer(containerView);
        displayView(position);
    }

    private void displayView(int position) {
        Fragment fragment = null;
        String title = getString(R.string.app_name);
        switch (position) {
            case 0:
                fragment = new HomeFragment();
                title = getString(R.string.title_home);
                break;
            case 1:
                fragment = new SomeFragment();
                title = getString(R.string.title_something);
                break;
            case 2:
                //fragment = new SomeotherFragment();
                //title = getString(R.string.title_somethings);
                break;
            default:
                break;
        }
        if (fragment != null) {
            FragmentManager fragmentManager = getSupportFragmentManager();
            FragmentTransaction fragmentTransaction = fragmentManager.beginTransaction();
            fragmentTransaction.replace(R.id.container_body, fragment);
            fragmentTransaction.commit();
            getSupportActionBar().setTitle(title);
        }
    }


    @Override
    public void setTitle(String title) {
        getSupportActionBar().setTitle(title);
    }


    public void setUp(int fragmentId, DrawerLayout drawerLayout, final Toolbar toolbar) {
        containerView = findViewById(fragmentId);
        mDrawerLayout = drawerLayout;
        mDrawerToggle = new ActionBarDrawerToggle(this, drawerLayout, toolbar, R.string.drawer_open, R.string.drawer_close) {
            @Override
            public void onDrawerOpened(View drawerView) {
                super.onDrawerOpened(drawerView);
                getSupportActionBar().invalidateOptionsMenu();
            }

            @Override
            public void onDrawerClosed(View drawerView) {
                super.onDrawerClosed(drawerView);
                getSupportActionBar().invalidateOptionsMenu();
            }

            @Override
            public void onDrawerSlide(View drawerView, float slideOffset) {
                super.onDrawerSlide(drawerView, slideOffset);
                toolbar.setAlpha(1 - slideOffset / 2);
            }
        };

        mDrawerLayout.setDrawerListener(mDrawerToggle);
        mDrawerLayout.post(new Runnable() {
            @Override
            public void run() {
                mDrawerToggle.syncState();
            }
        });

    }

    @Override
    public void onBackPressed() {
        super.onBackPressed();
        enableNavigationDrawer(true);
    }

    @Override
    public void enableNavigationDrawer(boolean isEnabled) {
        if ( isEnabled ) {
            mDrawerLayout.setDrawerLockMode(DrawerLayout.LOCK_MODE_UNLOCKED);
            getSupportActionBar().setDisplayHomeAsUpEnabled(false);
            mDrawerToggle.setDrawerIndicatorEnabled(true);
            mDrawerToggle.syncState();

        }
        else {
            mDrawerLayout.setDrawerLockMode(DrawerLayout.LOCK_MODE_LOCKED_CLOSED);
            mDrawerToggle.setDrawerIndicatorEnabled(false);
            getSupportActionBar().setDisplayShowHomeEnabled(true);
            getSupportActionBar().setHomeButtonEnabled(true);
            getSupportActionBar().setDisplayHomeAsUpEnabled(true);
            mDrawerToggle.syncState();
        }
    }
}

HomeFragment.java

public class HomeFragment extends Fragment implements View.OnClickListener {
    @Override
    public View onCreateView(LayoutInflater inflater, ViewGroup container,
                             Bundle savedInstanceState) {
        View rootView = inflater.inflate(R.layout.home, container, false);
        // Inflate the layout for this fragment
        fab = (FloatingActionButton) rootView.findViewById(R.id.fab);
        fab.setOnClickListener(this);
        ((TitleSetter) getActivity()).setTitle("Home");
        return rootView;
    }

    @Override
    public void onAttach(Activity activity) {
        super.onAttach(activity);
    }

    @Override
    public void onDetach() {
        super.onDetach();
    }

    @Override
    public void onClick(View v) {

        switch (v.getId()) {
            case R.id.fab:
                ((NavigationDrawerEnabler) getActivity()).enableNavigationDrawer(false);
                Fragment newFragment = new NewWord();
                FragmentManager fragmentManager = getFragmentManager();
                FragmentTransaction fragmentTransaction = fragmentManager.beginTransaction();
                fragmentTransaction.replace(R.id.container_body, newFragment);
                fragmentTransaction.addToBackStack(null);
                // Commit the transaction
                fragmentTransaction.commit();
                break;
        }

    }


}

AnotherFragment.java

public class NewWord extends Fragment {
    @Override
    public void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setHasOptionsMenu(true);
    }

    @Override
    public void onCreateOptionsMenu(Menu menu, MenuInflater inflater) {
        super.onCreateOptionsMenu(menu, inflater);
    }

    @Override
    public boolean onOptionsItemSelected(MenuItem item) {
        // Get item selected and deal with it
        /*Not even this*/
        Log.d("KEY: ", String.valueOf(item.getItemId()));
        switch (item.getItemId()) {
            case android.R.id.home:
        /* Doesn't execute*/
                Log.d("Fragment", "I'm here");
                getActivity().onBackPressed();
                return true;
            default:
                return super.onOptionsItemSelected(item);
        }
    }

    @Override
    public View onCreateView(LayoutInflater inflater, ViewGroup container,
                             Bundle savedInstanceState) {
        View rootView = inflater.inflate(R.layout.new_word, container, false);
        return rootView;
    }
    @Override
    public void onAttach(Activity activity) {
        super.onAttach(activity);
        ((TitleSetter) activity).setTitle("Text");
    }

También el diseño del cajón

<android.support.v4.widget.DrawerLayout xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools"
android:id="@+id/drawer_layout"
android:layout_width="match_parent"
android:layout_height="match_parent">


<LinearLayout
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:orientation="vertical">

    <LinearLayout
        android:id="@+id/container_toolbar"
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:orientation="vertical">

        <include
            android:id="@+id/toolbar"
            layout="@layout/toolbar" />
    </LinearLayout>

    <FrameLayout
        android:id="@+id/container_body"
        android:layout_width="fill_parent"
        android:layout_height="0dp"
        android:layout_weight="1" >

    </FrameLayout>


</LinearLayout>
<fragment
    android:id="@+id/fragment_navigation_drawer"
    android:name="com.calgen.wordbook.activity.FragmentDrawer"
    android:layout_width="@dimen/nav_drawer_width"
    android:layout_height="match_parent"
    android:layout_gravity="start"
    app:layout="@layout/fragment_nav_drawer"
    tools:layout="@layout/fragment_nav_drawer" />

Y menu_main.xml

<menu xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools"
tools:context=".MainActivity">

<item
    android:id="@+id/action_search"
    android:title="@string/action_search"
    android:orderInCategory="100"
    android:icon="@drawable/ic_action_search"
    app:showAsAction="ifRoom" />

<item
    android:id="@+id/action_settings"
    android:title="@string/action_settings"
    android:orderInCategory="100"
    app:showAsAction="never" />

De hecho, me referí a este tutorial para configurar el fragmento del cajón de navegación:Colmena de Android.

También mencioné preguntas similares respondidas aquí en stackoverflow:

1)Cambiar entre la imagen de Android Navigation Drawer y Up caret cuando se usan fragmentos

2. Mi problema es similar a esto:Indicador de presentación del cajón de navegación de Android para fragmentos de nivel inferior. - No pude comentar aquí ya que no tengo 50 repeticiones. Implementé lo que se dijo exactamente en los comentarios.

Pero aun así, al hacer clic en el cursor hacia arriba no se ejecuta la función onOptionItemSelected, a pesar de que tengo el botón de inicio habilitado.

Ahora estoy agregando mi styles.xml personalizado, ¿puede haber algún error en esto?

<?xml version="1.0" encoding="utf-8"?>
<resources>
<style name="MyMaterialTheme" parent="MyMaterialTheme.Base"></style>

<style name="MyMaterialTheme.Base" parent="Theme.AppCompat">
    <item name="windowNoTitle">true</item>
    <item name="windowActionBar">false</item>
    <item name="android:activatedBackgroundIndicator">@drawable/nav_background</item>
    <item name="colorPrimary">@color/colorPrimary</item>
    <item name="colorPrimaryDark">@color/colorPrimaryDark</item>
    <item name="android:textColorPrimary">@color/textColorPrimary</item>
    <item name="colorAccent">@color/colorAccent</item>
</style>
</resources>

También la barra de herramientas personalizada.xml

<?xml version="1.0" encoding="utf-8"?>
<android.support.v7.widget.Toolbar
xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:local="http://schemas.android.com/apk/res-auto"
android:id="@+id/toolbar"
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:minHeight="?attr/actionBarSize"
android:background="?attr/colorPrimary"
local:theme="@style/ThemeOverlay.AppCompat.Dark.ActionBar"
local:popupTheme="@style/ThemeOverlay.AppCompat.Light" />