Well, you asked "what delusion are they talking about", and I thought the text was quite clear about that, so I answered with what.

However, I do think the OP has unfairly bought Matt Walsh's trick here (and I do think it's a trick): it was Walsh, not Dr. Forcier, who brought up chickens. Dr. Forcier clearly doesn't want to go there ("does a chicken have gender identity?"--entirely valid question). This really does not look like a deeply considered opinion on Dr. Forcier's part.

However, once she does go along, she immediately says something really stupid: "We assume they [the chicken] are female if they lay eggs." (Of course, Walsh edited the video, so the exact flow may be different than it appears...I'm assuming for the sake of this post that this isn't a complete gotcha situation.)

If it is actually her considered opinion that it is an assumption rather than a classification that egg-bearing vertebrates are female, then that is, indeed, completely at odds with science. If, instead, she's thinking about defending gender identity in humans and has jumped over to chickens without bothering to clarify that the considerations very likely don't even apply because chickens do not, insofar as we know, have the same kind of rich mental lives that humans do (and she did start going in that direction, e.g. "do chickens cry"); and that sex and gender are not the same thing; well, that's an error on her part for not being more clear, but more of a simple misstatement than the kind of dogmatic irrationality suggested by the OP (and Walsh).