Is it possible to see what was 'illegal' about my app?
There is no way to gather more insight, other that what Apple tell you directly. Only Apple will be able to answer your question for more information.

Ask the Apple iTunes Connect team via the Contact Us details:


  App Review
  
  Find out the status of your app and submit general questions for the App Review Team.


Ask the Apple Review team via the appeal process:


  App Review Board
  
  The App Review Board provides the opportunity to appeal the rejection of an app if you believe that the functionality or technical implementation was misunderstood. You can submit additional details to the App Review Board to help them determine if your app should be reconsidered. Sign in to submit an appeal.