Was there any reason why the designers of Java felt that local variables should not be given a default value? Seriously, if instance variables can be given a default value,
The actual answer to your question is because method variables are instantiated by simply adding a number to the stack pointer. To zero them would be an extra step. For class variables they are put into initialized memory on the heap.
Why not take the extra step? Take a step back--Nobody mentioned that the "warning" in this case is a Very Good Thing.
You should never initialize your variable to zero or null on the first pass (when you are first coding it). Either assign it to the actual value or don't assign it at all because if you don't then java can tell you when you really screw up. Take Electric Monk's answer as a great example. In the first case, it's actually amazingly useful that it's telling you that if the try() fails because SomeObject's constructor threw an exception, then you would end up with an NPE in the finally. If the constructor can't throw an exception, it shouldn't be in the try.
This warning is an awesome multi-path bad programmer checker that has saved me from doing stupid stuff since it checks every path and makes sure that if you used the variable in some path then you had to initialize it in every path that lead up to it. I now never explicitly initialize variables until I determine that it is the correct thing to do.
On top of that, isn't it better to explicitly say "int size=0" rather than "int size" and make the next programmer go figure out that you intend it to be zero?
On the flip side I can't come up with a single valid reason to have the compiler initialize all uninitialized variables to 0.