I can really see why the gloves would annoy Elsa, and be really awkward for Anna. The gloves represent Elsa's unhappy childhood, and the containment of her powers. The gloves would not be a good thing to bring up.
While I love the "sisters before misters" theme, Frozen is CERTAINLY not the first Disney film with women who can hold their own. But let's just say Frozen is the one that unite the morals of all "I don't need a man and sisters first" movies