[Okashira]

Originally Posted by aka113

I agree can someone please explain

It's only a deduction, but...

Spoiler:

It looks like Tatsuya won't listen to anyone from his household and doesn't have a good relationship with anyone but Miyuki. Thus, if his household appoints Miyuki as the next head, there are chances that Tatsuya will stick along due to their close relationship, and thus he could be used as an asset to the family (which is obviously what they want).

This follows the idea that Miyuki will do what's she's told and what the family wants, of course. Also follows the idea that probably that Tatsuya wouldn't bother with his family at all sans Miyuki.