Sena, girl, I know that’s how it looks from the outside but their parents are incredibly shitty and controlling. Forcing their plans onto the eldest daughter, and once she managed to stand on her own and go against them, they want to force the younger sister (who is not fit to administrate cram schools AT ALL) to be their puppet now.
Everyone’s got their struggles bby
For most of history, assuming your kids would go into the same business as you would have been a reasonable assumption because what else would they do? And in this case, there is also a desire to pass the family legacy that they've spent a lot of time resources building up onto the next generation.
Or basically, they're just really stubborn and traditional, which results in them having a hard time understanding non-traditional stuff like mainstreaming of lgbt relationships. I would bet on them coming around once they realize the kids aren't going to fulfill their expectation and that they either have to adapt or end their relationship with both their children while still not getting what they want. IRL, even when parents go as far as to disown their LGBT kids, they tend to come around in a few years and want to have some type of relationship once they see the kid finding happiness and self fulfillment with them out of the picture.
These guys are not the best parents, but their behavior (supporting the kids in their studies, wanting to set them up for success in the future, etc) suggests to me that they actually do care about them and just can't understand why you'd pick something risky, uncertain, and likely to evoke hate/prejudice over the sure thing they've spent their whole lives setting up, possibly while giving up on many of their
own dreams in the process. They have a level of investment in all this that they're not going to be able to give up until they're forced to do so.
Edit: It occurs to me that, if the idea here is to arrange marriage her with someone who actually
is fit to take over the business, her actual love interest would be pretty good at it and is even already an employee. Of course, they aren't going to accept that for a while at least.