Lets say that you have a mate in 3 but you choose a different method that would have still lead to mate, such as a mate in 5. you are not seeing the correct combination that the tactic is trying to show you.
Or how about you win the queen instead of mating, that is another example.
I used to play on
chess.com and they have nice comments with their tactics that I read often, but I moved to chesstempo because it was better without time pressure. I learned exactly how to do tactics in a three step questioning process.
1. Is the king safe? Can I checkmate him?
2. Is the queen safe? can I trap her or do any other nasty tactics to her?
3. are the pieces safe? That piece is just hanging!