She probably sees your new sorority as a threat, especially if the fraternities are excited about it.
I'm not dissing service GLOs, but some people want the social aspect, too, and my national (which I'm sure isn't the only one) encourages us to do community service. In fact, my chapter *requires* 5-10 service hours per semester. There's no rule that says you can't help the community out AND be social!
Maybe you do need that girl's sorority's vote, but maybe her sisters don't feel the same way she does.