Bitcoin was invented for the same reason that dogs lick their balls, and the reason is... because they can.

Simple as that, the technology was there, the cryptography was there, the coding language was there, it was about get the idea, the tools and put it all together.

We don't have to break our heads asking this kind of question, the important thing is it was invented and why that happened doesn't matter at all, the real question is, how can we use it to make our lives better?