Your friend's argument is valid. However... vegetarianism is, from a biological standpoint, a survival-limiting behavior for humans. We are omnivores by evolution. Going vegetarian flies in the face of the genetic coding that leads us to consume whatever is available that doesn't actually poison us quickly - and we can learn to avoid foods that poison us slowly if they don't give us a short-term euphoric benefit. We can choose to go vegetarian, but it is a choice that conflicts with what our digestive systems are designed to do, and what our hindbrains drive us to do.
This is not a statement on the morality of vegetarianism, it is a statement of why I think vegetarianism is rare.
I understand why many feel that regarding sexism as innate is harmful, and it is harmful to a degree, the shellback conservatives will throw the "It's natural" argument in our faces. But if we don't consider the possibility, in my case, I think probability that sexism has deep seated secure roots that were sunk far before the modern era that are underestimated at our peril, we are in for an increasingly nasty series of shocks as we strive to eliminate it. And in terms of nasty shocks, as women continue to acquire more economic and political power, I do wonder if the worst is yet to come in terms of counterreaction.
For example: The current emerging cultural attitude in the US that belittles college degrees is growing at the same time it is sinking in to more people that women are more likely to get college degrees than men. I don't think this is a coincidence.
Many innate behaviors become harmful as the physical and social environment of an organism changes, and so the behaviors must change to make continued survival more likely. But changing a behavior which is a conscious choice is one thing, Digging into human hindbrains to chang emore deep-seated behavior is considerably more difficult. I am not saying it is impossible, and it is certainly desirable but... Well, look at all the fundamentalist religious movements around the world, differing wildly in structure and beliefs - the one thing they all seem to agree on is the common notion that women must be kept down in their place. An attitude that crosses a great number of social boundaries.
Again, I fully understand the reluctance to call sexism innate. However, innate is not immutable, it is "just" harder to change.
I freely admit that I am something of a cynic, no doubt this fuels my opinions on this subject.
But I am also something of an optimist, if sexism is the "I" word many do not want to use, I nonetheless believe it can be a changeable behavior.