Cyclops did have his time of doubt. There was a whole issue about it. He moved past it. Hell, you can make the case now that his enhanced emotions are making him too certain about himself.
But as been said before: Haters gotta hate.
It's not like they trusted her training to a guy with severe neuroses who would do something ill advised with massive, reality altering power like re-write history for the sake of giving some old bird a few more years. Especially if said guy had never stepped foot in K'un Lung and doesn't know the first thing about K'un Lung training.
It's hard for me to listen to people not in my position. A caterpillar can't relate to what an eagle envisions.
I think Emma is one of Marvel's number one characters, and one of their number one female characters. I wouldn't be surprised if she died, but Marvel has also been talking "oh we want to write more books with strong female leads" and such. Who knows.