1. It felt unnecessary to tie the characters together
Making Michael Burnham an adopted sister of Spock was a very shoe-horned idea. Nothing about her character, especially the one we left at the close of season five, felt anything like Spock. The emotional difference felt off, but there are also practical differences that truly stand out. First of all, she's a human and has different physical needs.
Humans are weaker, less gifted intellectually, and have a different sleep and food cycle. Thrusting a child onto Vulcan makes little sense from a story idea, as Spock's family would have to bend over backward to make Michael Burnham not only survive but thrive on Vulcan. That was the point, however, that she was such a gifted person that she hung with Vulcans on every level. This really irritated fans because that's not how science works. That's like writing a story where a human outruns a cheetah. It doesn't work.
But that's not all. Her being on Vulcan seemingly caused her to act like a Vulcan. Never mind Vulcans act the way they do because they're suppressing emotions so strong no human can comprehend them, but the way Burnham acted like a Vulcan felt wrong. At best it's a poor cosplay and at worst it's cultural appropriation.
If they had just not forced the connection and just written a new backstory for a new character, without shoehorning her into established lore, things would've been better. Being attached to Spock's history held her back creatively and it showed as the series went on. They clearly moved her away from those aspects of the first season character, and she worked significantly better as a character for it.