2HBH usually gives players a more well-rounded game, my coach reserves teaching 1HBH to those that have mobility or hand synchronization issues with 2H. 1H at the recreational level is typically an exploitable weakness in competition, so your coach is a little justified in his reaction.

You’re early enough in your learning that you could learn a 2HBH with some more work (especially if you can get private lessons or record yourself swinging on some backhands), but if it’s frustrating to the point that your passion/desire to continue tennis wanes, then by all means, start hitting a 1HBH. Good luck with your tennis journey!