This leads me directly to my point: her fear of admitting that people aren't doing things for the sole purpose of aggravating her because they hate her and love to see her suffer. Since Elly makes a point of not deriving the least bit of pleasure from her life lest she be seen as immature and foolish, she assumes that any bit of happiness that other people have is their way of sticking it to her. This means that if Michael were to do something he liked or grow to like something, he's doing it to torment her because he can't bear to see her happy.
We must also remember that she tends to regard any activity that doesn't somehow keep her from having to do housework or be a parent, force her to admit that Phil is more respected because he isn't a whiny defeatist or make her look like a big shot as being an evil that cannot be tolerated. If Mike doesn't want to spend his childhood being Lizzie's primary (if not sole) caregiver, he's a selfish, ungrateful brat who'd rather waste his time on some pointless, anti-mother irrelevance called "enjoying the only childhood he's ever going to have" than paying his poooor, put-upon parents back for not throwing him out into a snowbank. If Mike wants to play hockey, it's not because he likes it and wants to have friends, it's because he wants to torment Elly by forcing her to sit in a freezing cold rink. If Mike wants to play the trumpet, it's because he wants to become a bum instead of, you guessed it, wants to not pay his poor parents back for having to waste money feeding, clothing and housing him simply because they brought him into the world.
Finally, we have to remember that she's got it in her head that if a person isn't instantly good at anything, he's a failure who must quit at once. The idea of having to actually struggle to succeed horrifies her because it means that she can't wallow in self-pity and wonder why the world is unfair. Better to teach her offsprings to envy those with the will to dare and to do and call them selfish and arrogant than to admit that she's a bone-idle defeatist who wants to spite people by never even trying. Combine that with threatening to take what little privileges they have for not practicing and they'll grow to think of everything you hate as something awful and hard that they never want to do again.
The end result of all of this is that we have Michael spinning his wheels and thinking that he's fulfilling his own dreams and ambitions when he's actually more or less a ventriloquist's dummy having the literary career Elly lacked the courage and tenacity to have. The world was robbed of a man who could actually do something useful that he loved so that a gutless, selfish non-entity who could live her failed dreams through him as well as settle an old score with someone who won their childhood despite her being older and thus having more rights. In her eyes, this constitutes success because her own failings as a person and vindictive stupidity have been validated. It's like how constantly rubbing in the fact that she has better things to do than to protect Lizzie has created a passive, apathetic drone who'll marry who Mommy wants her to. Even better for Elly, Mike hates music and Liz wonders what she ever saw in figure skating.