Seeing as his point didn't have anything to do with gender, don't bring it up. Gavilar is the one to discover anti-light first, how, we don't know, but he is the first (Unless the shards know about their anti-tones, which I believe is hinted with Odium trying to convince Raboniel to find it, but either way, he is the first Rosharon, which is still impressive.) Navani does get credit for learning the method to creating it and then spreading that knowledge, which is impressive and I feel would give her some right to call herself a scholar, she is clearly adept at experimenting and connecting data, I don't see why she wouldn't be considered one just because she focuses more on guiding scholars then participating with them.
This is the only way it would acceptable after the sibling was basically given the choice bond her or die.
Leading and unifying are not the same thing, while they may share similarities. Dalinar has been trying to unify forces that would not normally cooperate and needs constant effort to keep together and not shatter. Navani, while a great leader, does not unify anyone that wouldn't have worked together. She guides the scholars, but they would be working together regardless, though perhaps less productively with someone else in charge. She orders the generals, but they would been working to launch a counterattack regardless, she simply gives them direction, not something small, but not really unifying.
the thing that needs to be clarified is that she isn't unworthy in general, but she isn't worthy of being a bondsmith, at least no more than any of the other leaders on the Council. To make clear what I'm saying, Szeth is incredibly worthy of a Highspren, he fits the order perfectly, but he is not worthy of, let's say, an Honorspren. Navani does not fit that order. She fits other orders, Elsecallers being the first to come to mind, but not Bondsmith.
Edit: I hate myself. So there is one moment where she does do what I say she doesn't and that's with the two members of the guild who at first refuse to share knowledge of how to transfer stormlight until she manages to convince one of them. The moment is small, but still there and should be taken into account. Not sure if that's enough, but it's definitely a point in her favor.