Hollo, your coach is telling you to throw short punches simply because you're throwing your shots too wide, just like your left hook like you mentioned. A lot of good trainers call right hands sucker punches (particulary leads) because only suckers throw them which is liable to get them countered. How much more easy is it to get countered if you throw your punches wide.

Your coach is right to correct it, because if I was your opponent and I knew you threw any of your punches wide I could see it coming anytime, which then I could drop you. Usually you don't throw your punches wide, becuase like I been saying it telegraphs to your opponent.

If you want elusiveness, work on controlling the range between you and your opponent, always move, circling and keeping your opponent away with jabs and counters, if he takes a step toward you then you shorten up the punches. I've seen fights in boxing and mma in which short punches in combinations was more overwelming than wide shots or flurries could ever accomplish.

If it doesn't feel natural, it's because short straight punches have to be trained, but once you mastered it it'll pay off big time. Fighters like Max Baer, and today's Samuel Peter both who hit like they got refrigerators in their fists were able to do so much more due inpart of throwing short straight punches.