In baseball, unlike basketball or football, once a player is removed from the game, he can't be put back into the same game. That is (probably) to prevent a repetition of matchups.
Example: Late in the game, you have a matchup of (lefthanded) batter X against (lefthanded) pitcher A. So the batting team replaces X with a right handed batter Y. The pitching team brings in B, a right handed pitcher. Now the batting team wants to use a left handed batter, but they can't "recycle" X. So they either have to use another left handed batter, Z, or let the new, unfavorable matchup stand.
My understanding is that there is an exception involving catchers. That is, if you replace a starting catcher with a second catcher, you can put back the starting catcher. What I'm not sure about is whether this is true generally, or whether it applies only in special situations.
Are there situations in which you can "recycle" a catcher (or other player) in baseball? And if so, why would that be the case?