Why can I lose more trophies than I win from a single battle?
The system assumes that the player with a higher amount of trophies will most likely win the match. For example, if player A (with a high trophy count) attacks player B (with a low trophy count) and loses, the system will move some of the trophies from player A to player B. Next time player A goes to attack, he will face easier targets while player B will be a target for even higher ranked players.
So if you attack a player with fewer trophies than you and lose the match, you’re going to lose more trophies than you would have gained if you had won. Making a mistake as a high trophy player has a larger effect on their rank than the same mistake would have on a low ranked player. High trophy players will need to play extremely well in order to preserve their trophies and rank.