I'm guessing your school or home computer had it on the right growing up? I got used to using it on the right because I didn't want to move the mouse to the left in the school computer labs as it was always a clutter of cords. At home half my family was left handed and mainly the PC was used by the lefties so I got used to playing FPSs with the left hand. I kinda hate playing on PC now because WASD is trash left hand mousing and it's A HUGE PITA to remap every single key to make sense on the the other side of the keyboard, some games don't even let you map keys like ';' because IDK, fuck me I guess.
I didn't really use a computer until my 1st year in college. And I didn't own a computer until I was 19, so I didn't learn to play FPS until I was in my 20's.
Before using WASD, I used WER and Space key for movement. Q=Jump, W=Forward, E=Strafe Left, R=Strafe Right. This allowed me to easily reach the number row and remap T=Chat 123456ASDFG for switching weapons and game controls. I switched to WASD with World of Warcraft, and use that for everything now mostly out of laziness and inertia (tired of rebinding everything, as you do).
I tried to use the mouse w/ my left hand and couldn't. Too much of the controls are right-hand centric. Keyboard shortcuts for browsing are all on the left side, etc. It does feel nicer to have it on the left hand sometimes.
I do think I'm more accurate with my left too.