Dagger: Without the dagger you lose Mat's whole motivation for at least 3 books. It explains why he acts the way he does for the first book, gives Rand a personal reason to chase the horn in book 2, and explains why Mat goes to Tar'valon in book 3 with the Aes Sedai who he dislikes instead of staying with Rand and Perrin who he is much closer to. It's also the catalyst to him getting his luck, although why is unclear. You definitely have to keep it.

Gender roles: Jordan gets a lot of unfair flack about "his views" on gender roles from people who don't realize that he's actually trying to subvert them. Don't listen to what a character says. Watch what they do. The boys will monologue about how the girls do this or that and then immediately go do that exact thing. The same is true in reverse. This is intentional. The vast majority of the time, when one of Jordan's characters is espousing some backwards view, the story goes on to show you that they're wrong. He doesn't beat you over the head with it though, so a lot of people miss what he's doing.