I agree with Soylent Green in that your coach told you to do this and you are. If you're having problems with it then you need to address him. He's there to help you and he wants you to succeed.
That being said my second thought is how strong are your fingers / forearms? The palm showing is the right way to to put your glove on. I teach my catchers the same thing and the goal is to catch the ball with your finger tips. We even work a drill where they have to toss back and forth only using thumb, index and middle finger tips to catch the ball. Probably wouldn't hurt to work those in somewhere with your practice.