I think a big issue with "though" coaching is what you're yelling about. I've had coaches yell at us to be sharper, ask us why we dropped a stunt and had to do it 10 more times, punish us with conditioning for messing up counts, and tell us we were practicing like a second place team. With those coaches, we've gone on to be stronger as a whole, push for better, improved ourselves, and placed well. The year I won Nationals was the year I had a coach that never backed off if we were preforming under our potential, and my favourite coach of all time.
When coaches get personal though, I find it much harder to accept what they are saying, and use it to make me better. "Why am I not surprised" isn't teaching an athlete work harder, it's telling them that failure is what's expected of them. Calling someone out for being loose in a dance is not the same as telling someone they look like a flailing animal when they try to dance. That's how insecurities are formed. It's so important IMO to focus on what is being done and why, leaving out any personal or just plain snide comments. It's literally difficult to look at someone when they make you feel bad about yourself, and almost impossible to form a bond with any coach like that.
I've had a coach dismiss me by excluding me from learning new skills, dramatically emphasizing that she was using me as a backup to her first choices, and telling me I wasn't capable of the very skills I threw the previous year. Though I wouldn't call it bullying, it wasn't just "tough coaching." My skills regressed over the year, and I felt excluded from the team whenever I stepped foot on the mat. I stuck through it though and this year on the same team, and a different coach, I'm flying level 6 baskets and pyramids for the first time. Instead of being told "I don't think you can do that" or "you don't do baskets," our new coach tells us when we're ready to try something new, and stays upfront if we're not up to par with her expectations. She yells way more than last year's coach, but it's about things that will make us better, not passive aggressive comments that just bring down our morale.
I think you need to be able to accept criticism if you want to participate in a competitive sport, but to be a coach, you also need to filter your criticism if you want good results.