I love this scene because, for me, it pinpoints a characteristic that I truly love about Regina. And it’s one that I think is highly relatable, too. You see, Emma’s got this raw power that Regina can not only identify, but can, quite literally, FEEL. She can see magic; sense magic; use magic. And Emma is borne from the “most powerful magic of all”. In that sense, Emma holds the key to power that Regina worked so hard for.
But more than that, Regina is angry that Emma’s “wasting” her potential. I think it speaks to who Regina is, at heart: she’s the woman who had to work twice as hard as everyone else to be half as good, you know? Remember the look on her face when she found out that the letter she thought was about her - the one she went to for a “boost”, that reminded her she was WORTH something, that she was BETTER than the person she’d been told all her life she was, that she wasn’t a disappointment - was actually about Zelena? She was crushed. Because Regina wants to be the best - not only to gain her mother’s approval (which, ultimately, she never had until the very moment her mother died in her arms) but also to feel protected, to feel safe, to feel like nobody can hurt her again.
Compare this, then to Emma, who not only HAS more innate power than Regina (or so we’re led to believe) but COULD use that to protect herself and DOESN’T. It stands to reason that Regina is frustrated - not only with Emma but with herself, too, for all the things she might do with that sort of power but has never been able to access within herself.
I think it’s really important that Regina is the one helping Emma learn to control her magic. And yes, the methods through which she does that might be a little harsh, but Regina simply doesn’t know any better. She was never cajoled, never taught with a gentle, encouraging hand. She was never told that she was doing well - even when she was - or congratulated on any successes she might have. And while that doesn’t make it right, I feel like Regina is only applying what she KNOWS gets results.
And it does get results.