I don't remember the exact dialogue.
In general, though, I don't think it was so much a matter of Giles not being able to "handle" something as it was the natural effect of a grown "daughter" doing things her own way -- and choosing her own partners -- rather than deferring to her "father" (figure). This is a perfectly natural process. They grow apart and clash while the daughter asserts her independence until, eventually, an equilibrium is reached. Fathers and daughters do this. At least, my father and I did this.
I'm not surprised that it was Spike who said this. No offense to you male Buffy fans, but I have observed that you men have this weird primal code thing when it comes to fathers and their daughters' suitors. You do this weird dominance thing. My mom and I used to snicker about it all the time back when my dad and my (now) husband and I were doing that little dance. That Buffy and Giles should clash over leadership (life) decisions and men doesn't surprise me in the least.
Makes me sort of nostalgic for all of those uncomfortable moments that are only funny in hindsight. 🙂