IMO Darcy's comment has a dual purpose. It's immediate purpose is to try to raise Bingley's standards, which I think Darcy considers amiable but too accommodating. If Darcy is trying to help Bingley raise his family's stature in the world, he must try to make him somewhat more fastidious.

But I think family pride has a role here too, even if Darcy would not admit it to himself. We have heard (or hear shortly after this speech albeit from Caroline) that Darcy's sister is very accomplished. Darcy does not want to accept Bingley's declaration that all young ladies are accomplished; it implies that any number of lesser females (like Mary Bennet? LOL) might suppose themselves comparable to his sister.

In saying what he says (and particularly in accommodating all Caroline's list) Darcy does seem to get carried away to a standard that Lizzy (most likely correctly) claims is impossible.