In the position below, I'm promoting my pawn. The app says promoting to a Queen is incorrect, but a Rook is correct? In this setup it doesn't make sense.
[FEN "8/1P6/3N4/8/8/3k4/r7/4KN2 w - - 0 1"] 1.b8=R 1-0
If you promote to a queen with 1. b8Q, black has:
1...Re2+ 2. Kd1 Rb2
attacking the queen and hinting at mate with Rb1++. If white takes the rook 3. Qxb2 it is stalemate.
Because of the mate threat white does not have any other good square for the queen either (no good check and no square that would defend b1).
If you promote to a rook, black does not have this defense, because after 3. Rxb2 it would not be stalemate. The resulting endgame (King, rook and two knights vs king and rook) should be a reasonably easy win.
Also you need to know that if the queen gets exchanged for the rook (e.g. after 1. b8Q Re2+ 2. Kd1 Rb2 3. Qb5+ Rxb5 4. Nxb5) , the endgame (king and tow knights vs king) is draw.
For the same reason white cannot postpone the promotion because black has (at least) a draw if he can give his rook for the pawn (e.g. after 1. [random non-pawn move by white] Rb2 2. [random move] Rxb7).
Lastly, any other underpromotion (to knight or bishop) does not work either, because black will win the piece on b8 in the above line after 2. ... Rb2 because of the mate threat on b1.
So the only way to play for a win is by promoting to a rook.
The Lomonosov 7-man Endgame Tablebase shows the following. With the Queen, after the following...Re2+ Kd1, Rb2 Black king is stalemated.
Link to Lomonosov 7-Man Endgame Tablebase http://tb7.chessok.com/probe
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