Ok so I know that the (simplified) equation for force is $F=ma$, but here is what I don't grasp. If given that to get more $F$ you need either more $m$ or more $a$, then how come, if I'm pushing something e.g.: let's say I'm arm wrestling with someone, and I "lock" my arm, meaning that I'm not pushing forward just staying in place, how come I can resist his force, if I'm not increasing either my mass or my acceleration?
$F=ma$ is a little too simplified. It's really $\sum F=ma$: the sum of the forces acting on an object is equal to its mass times its acceleration. You have to account for all of the forces involved.
You can resist someone who is arm wrestling you because you are using your arms to apply a force to your hand in one direction, and your opponent is using their arms (and hand) to apply a force to your hand in the opposite direction. If the forces happen to be exactly equal in magnitude, then the sum of the forces is 0, and you have no acceleration.