Why does it end in a stalemate if all my pieces are alive and they have none? That’s not a stalemate, I can move freely and get them.
In chess they cannot move onto a spot that would put them in check. If they can make no legal moves, it's a stalemate.
That is a standard rule in chess. If your opponent has no legal moves (i.e. no way to move without moving his king into check) and is not currently in check, it is considered stalemate, which is a draw.