I don't think that's it, or Itsuki wouldn't have asked the relationship question.
Fuutarou's response was clearly not what she was looking for, and so she doubled down on distancing themselves. The only thing that really makes sense in this context is the issue Miku has had with feeling friend zoned, a sentiment even Nino echoed when she said that she'll make Fuutarou see her as a member of the opposite sex. But while I can see why Ichika, Nino, and Miku would be on board, I'm not sure why Yotsuba and Itsuki would be bothered by it. Unless they are just acting in tandem with the wishes of their sisters?
The only other thing I could think of is that Nino informed everyone of Fuutarou's dropped grades. But while that gives a mechanism for why the quints would want him to stop being their tutor, it does not explain why the first thing out of Itsuki's mouth about the situation concerns their relationship.