Why must I learn proofs 
Why is my crazy math professor doing all these proofs?  I don't need
to know this stuff!  I don't care why it's true!  

Firstly, there is a practical reason to learn 'why' things are true.
The world is quickly moving to a place where the knowledge of
individual facts, such as knowing how to solve a particular problem,
isn't going to mean much any more. (Because of instant access to facts
via Google for example.)  Understanding the 'why' of facts, and the
process that led to these facts WILL matter, because *that* knowledge
can lead to the solution of new problems.

But there are other reasons for studying proofs also.  Proofs are
logical arguments, with a high degree of rigour.  Logical thinking is
a knife for cutting through many problems, and the study of proofs
sharpens that knife.

Finally there are aesthetic reasons.  You might learn proofs for the
same reason your english professor makes you read Shakespeare.  Such
studies may not be of any (direct) use to you as career training, but
they expose you to the greatest of works and ideas.