Why do I lose Trophies despite the attacker not destroying my Gate?

The only way you can earn Trophies without destroying the Gate is if the other player has significantly more trophies than you.

If you pay out a large sum of Ambrosia and Gems to take this person out, and make it to the gate, despite them being way above you in both ranking and level, we believe you deserve to get at least something. It keeps the game competitive, and it will always be much more beneficial in the long run to actually take the island.