My wife announced that she wants to sleep with other people. She claims that our sex life is bad, and she is not satisfied. We had incredible sex just the night before and she thoroughly enjoyed it. I know her, and I know when she is faking and she wasn’t.
I don’t know what to do. I don’t want her to cheat, but she is convinced she won’t be happy until she gets to sleep with someone else.
LemonVibe 
I’m sorry, it must be hard to have her say that to you. Unfortunately there is nothing you can do if she wants to do that, all you can do is be honest about how you feel about it and what the results will be if she does. Also, make it clear that you want to address the issue itself and want to do what you can to give her what she wants without going down a road that 1. you can’t come back from and 2. that could end what you do have together. She is clearly needing something but maybe it isn’t what she thinks or it is but maybe not at the cost of what she currently has. I’m sorry, this is difficult and I don’t want to suggest one way or the other as I don’t know you or her but all you can do is be honest about yourself and what you want in your life. You can’t force her to do / not do something but at least know that whatever she chooses will reduce the stress of not knowing what happens next.
I know this is difficult for you, but coming from a woman, I sort of understand her view point.
Please don’t think it’s necessarily her wanting to cheat. I was at the same point with my husband at one time. It happens. Hopefully she will come out of it without having to find relief in someone else, but if she doesn’t and she decides to go behind your back, then she obviously not doesn’t feel for you the same way you feel for her…
I think that you two may need marriage counseling and to do a lot more talking and thinking about this. You both have a lot of questions to answer and may or may not be compatible in the long run.
Do you want sex outside the marriage?
Do you care if she does?
How do you both feel about swinging? Polyamoury? Etc.
A third neutral party may help you both.