I've been playing online FPSs for years now, but I've always been absolutely terrible at them. I can maybe get a 1:1 K:D ratio on a good round, but my average is probably closer to 1:3 or 1:4. This has been pretty consistent in every FPS I've played over the years. I'm not sure what I'm really doing wrong. I use cover. I try to flank with my teammates. I throw grenades to flush enemies out of cover. But somehow it always seems like they're faster, more accurate, better able to get the drop on me.
Is it just because I only play them for a few weeks or months before moving on? Is this something that gets better with practice, or do I have some kind of undiagnosed motor deficiency?
Connection is a pretty big deal and a lot of modern games manage to hide a terrible connection pretty well. Chances are that's your issue.
Map knowledge is what makes a good player though, especially on PC where aiming and shooting is pretty easy. I use to be pretty good at COD and it was just because I figured out how the spawns flipped. In Battlefield I just learned the routes people took and where to check for campers. I admittedly wasn't great at CS, but I got a lot better when I learned how and where to peek. You do kind of have to get to the point where map knowledge is intuitive though so it does require a lot of playtime and it's not worth it.
Also most FPS games aren't designed to be cooperative. It helps in some of them, but for the most part it's bad for you.