I've actually asked myself this exact question a few times, and while I can think of a few smaller reasons for liking shooting/firearms, I can't seem to figure it out exactly, I just do. The first time I had ever fired a gun was when my dad let me shoot his S&W model 18 revolver, and from then on I was hooked.
I think it party has to do with my liking of loud noises, ever since I was a kid I've always had a fascination with loud noises like fireworks, don't really know why. Part of the reason I like shooting my mosin and M1 Garand so much is because of the loud boom-like report they create, as well as feeling the concussion. Not sure if anyone else shares this. This definitely isn't the sole reason I like shooting though, as I enjoy shooting my .22 more than anything. I guess as others have stated its just a fun and relaxing challenge trying to hit small targets, or shooting a tight group. I also enjoy shooting at reactive targets, like gallon jugs of water, aerosol cans, and anything else that has a cool effect when a bullet hits it.
For me though shooting is only part of the fun of owning a gun. I also enjoy sometimes just holding and admiring my guns, especially the M1. I bought my mosin and M1 mainly due to their historical significance (they also happen to satisfy my need for loud booms
), I like thinking about where they've been, and what the person(s) were like that used them in the past.