ORIGINAL: MinnFlyer
Typical of a trainer.
Want it to stop climbing? Slow it down.
Want to fly fast? Get rid of your trainer and get an intermediate plane
As MinnFlyer said, it is what trainers do. The tendency to climb when throttled up is part of what makes a trainer a trainer.
When a student panics and hits the throttle the plane climbs. When you get disoriented and get into a dive as the plane build up speed it will automatically pull out of the dive, again because of the climbing tendency.
Add to that the dihedral and high wing combination and the plane wants to fly upright.
Add everything together and it makes an easy plane to learn on. It is designed to do these things.