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Baseball has used the terminology for at least 75 years because it's an easy way to convey the type of loss streak you can afford to absorb in order to bring you back to .500. 12 losses gets you to back to .500 at 53 and 53.

What you're doing instead is comparing the team to it's mythical self. It's the same the way division rivalry games can't ever any different result (for the division as a whole) than a .500 balance.

Your observation has been joked about by sports statisticians and writers for decades. Dave Barry did a good "3 Games under .500" article that is pretty funny.
The owner's team is 40-43 and he starts going down your thought process.
So 41.5 and 41.5 would be .500 right?
So the owner told the manager he'd better figure out what to do in the next 1.5 games or he was going to fire him.
Then the manager gets confused about his middle relievers.
And so on...

Basically, half-games are a fuzzy concept for the general public.
A pure math or scientific context of "above .500" allows for fractions.
Baseball's context means differential in full games since that is tangible to the audience.

been asking the same question for about 30 years...

Yoda, your explanation actually makes perfect sense, especially if a winning season is the base measure of success. I'll look up that Dave Barry piece.

Technically, however, tack-ny is still right. Although the longevity of the terminology is well-established, it doesn't diminish the fact that it's still wrong. Twelve games above .500 should mean twelve games above their particular .500 average. Their particular .500 average would include halving their total number of games played. For instance, say a player only had 10 at-bats, and had 3 hits out of the ten. That would be an even .300 average. Then pretend he was 4 for his next 4 at-bats. Would you say he's 4 hits above .300? No, because if he was 0 for those last 4, his average wouldn't be .300, it would be 3/14 = .214. So he's really 4 hits above .214, which is a ridiculous thing to say. Believe me, I understand the reason for its common use. But it's still not very accurate.

Peter Angelos has defined "above .500" as the failure to lose all 162 games in a single season. Losing all 162 games would be a "perfect" season in Peter's dictionary. To be on point, however, I subscribe to Yoda's explanations in his two posts.