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?
To get the best thing out of something, one needs to know the history, reason, and origin of a thing. An antique can't be evaluated if its history is unknown. Tools cannot be used to their maximum potential if we don't know why it is made or created. Just like a bottle opener, can you use its maximum potential if you don't know that it is made to open a bottle? History, reasons, and many other things are important in maximizing the potential and usage of Bitcoin. It is one factor that made Bitcoin special. So I think knowing the reason for Bitcoin's existence is important. Because from that you can plan ahead on how to use Bitcoin to make our lives better.