I didn't start out writing my own system (I mean, I did, then it was a lot of work, so I started hacking instead), but my hack got out of control and I decided to go back and break from compatibility for the sake of internal consistency. So my "BRP hack" is now "inspired by BRP" I guess.
Largely, I wanted something which gave me small character improvements through play (organic skill-ups over time) and a classless framework to build tons of different characters into.
I needed something flexible enough to play merchants and politics, adventures and warfare, investigations and heists - but mechanically simple enough I'd actually run it. So, like most folks who get to hacking, I made a thing that works for me and have set about making it sensible and coherent enough for other folks to use.
I tried using straight BRP/D&D and derivatives with some house rules but it kept snowballing til a system-of-its-own was warranted. That also came with freedom though, because I was able to weave the world's magic into and through so much more than I could just hanging it on existing systems!
I tend to really like settings with their own systems, but I also buy a lot of system-agnostic settings, so /shrug