"...a lie about having a vasectomy does not?! WTF?"
I haven't seen the video yet so I don't know if they covered the background to this. Sorry if I'm repeating anything that was in the video.
If a woman consents to have sex with a man on the condition that he wears a condom but he then removes it without her knowledge that removes her consent.
The reason for this is that she has only agreed to have sex with a man while using a condom. She has not consented to sex without a condom.
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In contrast, with the alleged vasectomy case, the Court of Appeal said that the woman had agreed to have sex without a condom. The issue then was, as the court put it, "the nature of his ejaculate".
She had agreed to have unprotected sex with him but he had lied as to "the nature of his ejaculate" and she got pregnant.
The Court said that him not telling the truth about a vasectomy was not closely enough connected with the act of having sex as to have removed her consent. She had agreed to have sex with a man without a condom and that is what happened.
You might argue "I wouldn't have had unprotected sex if I'd known" but the Court has long held that a "but for" test is not sufficient to remove consent. eg "If I'd known he was married I wouldn't have had sex with him" or "If I'd known he was a policeman I wouldn't have had sex with him".
There is a link to the case here:
R v Lawrance [2020] EWCA Crim 971