For me, it's mostly about the texture. I like meat toward the rare side because it tends to lose flavor and get dried out as it's cooked, but it has to be cooked enough to have that "cooked" texture to it. If it's still raw in the middle, it's still kinda chewy and stringy, which I don't like. Obviously there are some cuts of meat that are really tender regardless, but I'm talking about a sirloin, ribeye or other everyday steak, not freakin' filet mignon.
If I cut into it and find I have to saw through it while holding it down with my fork, it's not cooked enough.