I'm not sure what discussion you're referring to, but you might be thinking of safe spaces, or at least a similar idea. The reason that in these conversations marginalized people get to speak whereas the majority are told to stay quiet is because marginalized people don't GET to speak most of the time. Women and homosexuals and racial minorities will often silence themselves in order to keep from drawing any ire from the majority. That's the whole majority/minority dynamic. The reason the privileged group (such as straight people or men or white people) need to stay quiet is to give the minority group an actual chance to say what's on their mind. The privileged group gets to say their side of it EVERY DAY, their side is the default (hence, privilege). I know this offends you but you need to consider the fact that minority groups don't usually get a chance to speak freely. It's not any sort of rudeness or lack of consideration against you, it's just about giving them a chance. The privileged group doesn't always NEED to add their input, their input is already injected by society because they're the majority.
This is pretty much what I just said, but it bears repeating--she doesn't get to give her view in everyday society. Her view isn't represented in the media and it is isn't represented in mainstream culture. Yours typically is. This is why you need to LISTEN to what minority groups tell you, because you don't normally hear their side ever. They hear your side every day. You're exerting your privilege as the majority by insisting they are required to hear your side too. Just try listening to them, I can't emphasize this enough.
I think you do care about what minority groups have to say, but I also think that you are too concerned about making sure the majority viewpoint is heard. The majority viewpoint is already heard and understood. This is all about giving the minority a chance to speak up WITHOUT having the majority viewpoint overshadow theirs like every other day of their life. To put this a bit more harshly, it's not all about you.
Maybe I should clarify further, When I refer to people as part of a minority or majority. I kind mean individuals within that group. When I meet someone that's better off and has more influence on the world than I do, and I have a discussion with them on a person to person (or even a small discussion group), I'll still let them speak. Because while they might be part of a powerful group that regularly speaks their mind but I don't think of them that way, I think of them as an individual. I suppose in a odd perspective that everyone is vaguely a minority in the sense that they are the only person that is... themselves. ugh I lack the graceful words to describe this but I imagine you know what I mean.
The majority and minority are both a group of individuals. They are not hiveminds where one hivemind has more strength than the other and is actively trying to bully the smaller one. They are groups of individuals. And individuals should be permitted to speak their mind, especially when they are caring enough to participate in a discussion about individuals that are marginalized.
I don't think of people as just a group. To put it in a minorly cynical way: We are not as connected as we like to think. We all live as ourselves alone and we die alone.