I've decided that I want to stop using phrases like, "So-and-so is an adult" or "We're all adults here" because:
1. Saying that you or someone else is an adult in certain contexts can imply that children are less deserving of respect, privacy, freedom, or whatever you are talking about. Of course there are some things that children can't do on their own, and it is understandable to use the "I'm an adult!" argument with your parents/guardians to mean, "I'm now capable of doing something that I couldn't when I was younger, so I should be allowed to do it," but there are also plenty of times when people say that it should be okay to eat what you want, dress the way you like, keep your living space the way you want, and basically make your own choices because you are an adult. This is not okay because it implies that children shouldn't also get to do these things. You should be able to do these things regardless of your age - there is no reason that being an adult needs to be a part of it.
2. Saying that someone should be able to handle something because they are an adult is not okay because it puts pressure on someone to "handle" or be okay with things that they might not be okay with at all and might not be willing to do. It imposes standards on the person because of something they didn't even choose (you don't get to decide how old you are). "Act your age," is commonly used to pressure people to behave differently than they want to behave. There is also an implication in such statements that children are not as good as adults, because saying, "If you act this way, you are not really an adult," clearly implies that you should behave like an adult and that it would be bad to behave more like a child.
3. I don't like using the word "adult" or "mature" in place of what we really mean to say, because these words are full of social standards and discriminate against children. I would much prefer to say what I really mean, such as, "We are all respectful enough to listen to this talk without making fun of the speaker," "We all have enough knowledge of the situation to make our own choices," or "We are all able to give consent because we have an equal, trusting, consent-conscious relationship without twisted power dynamics that would make us feel like one of us has to obey the other when we don't want to." There are plenty of adults who would not be respectful, there are plenty of peer-relationships that do have messed up power dynamics, and that last description makes it clear that consent is not about being "mature" but about not having other people in power over you.