By default Volley uses the built-in AndroidHttpClient on systems that are < Gingerbread and HttpUrlConnection on newer. For some this may not be enough. Someone may need Cookies support, other may need to work self-signed SSL certificate. Probably there are few more reasons to use external HttpClient but most prominent one is that you may have old code that relies on it.
About 2 years ago I wrote Using newer version of HttpClient on Android (like 4.1.x). Now as follow up I added an example how to use Volley with such external HttpClient in my Android Volley Examples project.
Basically all I had to do is to create a new class ExtHttpClientStack, copy the functionality from the HttpClientStack and redirect all method calls from the built-in HttpClient to the external one.