The question was "Should we now teach our children that girls can be boys and boys can be girls and both men and women can have babies", so I think the question was aimed more at the idea of changing sex, not explicitly about self-identification of gender identity.
I think Germaine Greer was the only member of the panel who came anywhere near to answering the question.
Germaine Greer said "I believe that sex is real. I believe that you're born a boy or a girl, if you want to use those terms, and you've got lots of things that you have to deal with, especially if you're a girl, but also if you're a boy; and you may find that the way that your role is set up in society doesn't suit you at all. You may really want to be called a different name, you may really want to live a different life. You want to chose another role. Now, you've always been able to be a boyish girl or a girlish boy. Now, suddenly, if you are a boyish girl, you're being encouraged to think you're actually a boy which, as far as I'm concerned, is a mistake".
The other panel members mentioned: we now accept homosexual people and gay marriage, people trapped in an alien body, we are all people, people can change sex, we must move on, moral panic, Donald Trump etc.