[Note that in Firefly Fluxx, the Surprise You Can’t Take This Guy From Me has a similarly retaliative function as It’s A Trap, though the punishment is different. All of the same issues might arise with that card as with It’s A Trap!]
Player 1 played Steal a Keeper. Player 2 played It’s A Trap, then Player 1 played Belay That.
Player 1 believes that Belay That cancels It’s a Trap as if those two cards never got played, so the original Steal A Keeper stands, and Player 1 gets to steal a keeper from Player 2.
Player 2 thinks that when Player 1 played Belay That it should have then stopped Player 2 from stealing a keeper from Player 1, but that’s it. It should have been a wash and nobody got to steal from anyone.
A: Player 1 is correct in this case. Here’s how that works:
Player 1 played Steal A Keeper (an Action) to steal Player 2’s Keeper
Player 2 played the It’s a Trap (a Surprise) to prevent the steal and steal a Keeper from Player 1 instead.
Player 1 then played Belay That (a Surprise) to use its Surprise-countering ability to counter It’s A Trap. In this case, Belay That is not countering an Action, it’s countering a Surprise. It counters the entire card as if it had not been played, not just the counter-steal part of It’s A Trap, so Player 1’s original Steal A Keeper goes through unimpeded.
In fact, Player 1 could have played ANY Surprise to counter It’s A Trap, not just Belay That. They could have played Canceled Plans, or Veto, or That’s Mine, since all Surprises counter other Surprises. In fact, if Player 2 had had a second Surprise of ANY type, they could have played it to counter Belay That, and their It’s A Trap would have gone through unimpeded.