Can you move a piece with two hands? Can you pick it up with one hand, transfer it to the other hand, and then place it on a square? Which hand must be used to press the clock? Both?
Because that's EXACTLY what you are doing if you use two hands to promote a Pawn. You are using two hands to move a single piece, switching hands partway through the move.
In over-the-board chess, at least in tournaments following official rules, there are several rules regarding how many hands you can use to perform certain actions.
The most prominent example is that you cannot move a piece with one hand and press the clock with the other hand. These two actions have to be done with the same hand. This makes sense: If you were to use two hands it would be pretty much impossible to see if you are cheating, ie. pressing the clock a fraction of a second before you finish your move, which would rather obviously be a rules violation.
A similar rule pertains to castling: You must castle using only one hand. You cannot castle using both hands to move the king and the rook at the same time. While the reason for this might be slightly more up to opinion, I suppose it still makes some sense: After all, there's also the touch rule: If you touch a piece you have to move it. Thus, if in this situation you would touch the rook before the king, that would mean that you must move the rook only. If you were using both hands to castle then it would be harder to enforce this rule because it would be hard to determine if you touched the rook before the king.
(One could still disagree with this interpretation, though. After all, the rule could be that if you lift both the rook and the king from the board, you are signaling your intent to castle, and there is no ambiguity involved. It could perfectly well be considered a rules violation only if you touch the rook, move it to its destination square and only then do you move the king. But anyway, maybe it's just simpler to keep the touch-rule as it is, and thus the castling rule as well, to remove ambiguity.)
What's less clear is why the one-hand rule also applies to promoting a pawn. Also here you must only use one hand to move the pawn and replace it with a promoted piece (although, as far as I know, here you can do it in the opposite order, ie. you can put the promoted piece on the final rank first, and then remove the pawn from the penultimate rank, as if you had moved it to the final rank.)
Why cannot two hands be used for this? What other rule could be (accidentally or intentionally) broken by using two hands to promote a pawn? Why does the one-hand rule apply to this case as well? What is it preventing?