If he is a chairman then there is an entire board of people who can replace him if Mei didnt want to do it.
She does want to do it and he wants her to do it. They want it kept with the Aihara's and their values.
If he lost trust in Mei he could choose someone else though.
Again, the entire point of a Mukoyoshi is for the husband to take over the position due to the patriarch need for male leadership. If this is a mukoyoshi then Mei isnt getting the chair position.
Not entirely true. He can marry Mei, become an Aihara instead of her joining his family, and she can still become the chairperson. The point of this is the position stays with the Aihara's but Mei gets the backing of his family because of the marriage. Her being young would make such connections valuable (for instance, without that she might look weak, lose the trust of the board and get replaced).
I just want to make it clear that mukoyoshis can be done without the daughter marrying the adopted man in order to keep the company in the family.
Unlike the marriage, that would only make sense if he were being chosen to take over the position. That's not what the grandfather chose him for.