Why does AP Computer Science A use Java? What are the reasons that AP Computer Science A is using Java as its programming language?
While Java is a great language in general, it has high verbosity, which is quite important for a timed exam.
How about other programming languages, perhaps something more modern, like Rust, Go, or Dart? Or even C++?
Particularly since they have recently removed interfaces and abstract classes, I would say that there are no particularly important philosophical reasons that they are using Java.  At this point, it was a historical decision.
The exam began in Pascal, and when they looked for a way to move towards Object Orientation, they switched (in 1996) to C++.  This was controversial at the time, as Java was very modern and was thought by many to be a conceptually better language, particularly for students.
They switched from C++ to Java in the 2003-2004 school year largely for two reasons:

Java was considered to be a better object-oriented language, particularly with regards to inheritance, and the compiler does a much better job at checking to make sure that beginners aren't doing silly things that they definitely shouldn't be doing.
College programs around the country were taking up Java, so it better reflected the reality of the introductory courses that students would be getting credit for.

You can read the justification for the switch to Java courtesy of the ever-magical wayback machine.
Given the recent changes to the AP Test, it does not appear that there is any particular good pedagogical reason to stick with Java at this point.  In fact, the latest iteration of the test basically ignores the most important features of OO, instead emphasizing a great number of imperative concepts.  However, the testing language is unlikely to change any time soon, as Java is still the dominant language at universities for teaching introductory Computer Science, and these are the institutions that must agree to provide credit if the AP exam is to continue to provide value.