"If women get boxed in by patriarchy, so do men," Gillespie said.
Her speech, which followed a cultural fashion show, ended this year's Ebony and Ivory Week.
Other events of the week included a discussion on what it means to be an American, a talk led by individuals with disabilities and a presentation on racism and sexism.
In her speech, Gillespie emphasized the need for different groups to unite in their struggles.
"If we're going to attack oppression, we've got to do it all, not just a little," Gillespie said.
When racism is discussed, all groups need to get involved, she said: "We don't come together around the issues as we should."
She went on to talk about how those in power stay on top by dividing their enemies and pitting them against each other. "That's how racism works," she said.
Black Caucus Vice President Takkeem Morgan expressed his concern that with the divide-and-conquer mentality in mind, it becomes difficult for the black community to address its own problems.
"Certainly it's a risk, but I think our silence kills us," Gillespie responded.
Different groups must come together and work for common goals instead of separating, she said.
Assata Richards (graduate-sociology) talked about how her efforts to improve the Penn State curriculum incorporate this idea.
"What we've tried to do is empower students to build their own communities," Richards explained.
"Don't just be together for this one week," Gillespie said, "This is your world and your time. Claim it."