There are multiple things that could be wrong with your friend's response.
As regards the first of these, the three situations are indeed very closely analogous. (Not exactly -- you chose different arguments in the different cases. A: ill-defined, ugly-history, no-good-measure, within-versus-between. B: ill-defined, ugly-history, within-versus-between. C: ill-defined, ugly-history, no-good-measure.)
As regards the second, I think not so closely. For instance, so far as I know the notion of strength doesn't have at all the sort of ugly history that the notion of race does, nor the (less ugly) sort that the notion of intelligence does. (Maybe it has a different sort of ugly history, something to do with metaphorical use of "strength" by warmongering politicians perhaps.) And I bet you can get something nearer to a usable culture-independent test of strength than to a usable culture-independent test of intelligence. And, as I said earlier, I greatly doubt that there's more variation in anything anyone expects to be a matter of strength within strong/weak than between those groups. (Incidentally, you wrote "more variation between ... than among" which is the wrong way around for that argument.)
I'm not sure how much we should care about the third and fourth of those points since I think we agree that the conclusion is dubious at best in each case. But for sure the context is different (e.g., one reason why people who think there's no such thing as race or intelligence bother to say so is that there are other people saying: oh yes there are, and look, it turns out that this traditionally disadvantaged race to which I happen not to belong is less intelligent than this traditionally advantaged race to which I happen to belong; nothing like this is true for strength) and it seems like that makes a relevant difference. (E.g., your friend's response to the comment about strength seems weirdly aggressive for no reason; in the case of a comment about race or intelligence, there's at least an understandable reason why an otherwise reasonable person might be touchy about them.)
So no, I don't think the situations are perfectly analogous, though they're close. If we consider only the first kind of error, then the analogy is pretty good. And if you were making an explicit argument then that would be OK. But you aren't; you're presenting your parody arguments, and inviting readers to point and laugh and draw their own conclusions. And if one of the parody arguments is laughable for reasons that don't correspond to defects in the arguments you're parodying (e.g., because it depends on saying that there are lots of scientific articles out there saying that strength is purely a cultural construct) then you're inviting readers to conclude that claims like "race isn't real" and "intelligence isn't real" for terrible reasons. It's like dressing someone up in a clown costume, getting them to present an argument, and saying "wasn't that silly?". The argument may well be silly, but it will feel sillier than it is because of the clown suit.
I agree with 99.999% of what you say in this comment. In particular, you are right that the parody only works in the sense of the first of your bulleted points.
My only counterpoint is that I think this is how almost every reader will understand it. My whole post is an invitation to to consider a hypothetical in which people say about strength what they now say about intelligence and race.
The concept of strength is ubiquitous in our culture. It is commonplace to hear one person described as "stronger" or "weaker" than another. And yet the notion of strength is a a pernicious myth which reinforces many our social ills and should be abandoned wholesale.
1. Just what is strength, exactly? Few of the people who use the word can provide an exact definition.
On first try, many people would say that strength is the ability to lift heavy objects. But this completely ignores the strength necessary to push or pull on objects; to run long distances without exhausting oneself; to throw objects with great speed; to balance oneself on a tightrope, and so forth.
When this is pointed out, people often try to incorporate all of these aspects into the definition of strength, with a result that is long, unwieldy, ad-hoc, and still missing some acts commonly considered to be manifestations of strength.
Attempts to solve the problem by referring to the supposed cause of strength -- for example, by saying that strength is just a measure of muscle mass -- do not help. A person with a large amount of muscle mass may be quite weak on any of the conventional measures of strength if, for example, they cannot lift objects due to injuries or illness.
2. The concept of strength has an ugly history. Indeed, strength is implicated in both sexism and racism. Women have long been held to be the "weaker sex," consequently needing protection from the "stronger" males, resulting in centuries of structural oppression. Myths about racialist differences in strength have informed pernicious stereotypes and buttressed inequality.
3. There is no consistent way of grouping people into strong and weak. Indeed, what are we to make of the fact that some people are good at running but bad at lifting and vice versa?
One might think that we can talk about different strengths - the strength in one's arms and one's legs for example. But what, then, should we make of the person who is good at arm-wrestling but poor at lifting? Arms can move in many ways; what will we make of someone who can move arms one way with great force, but not another? It is not hard to see that potential concepts such as "arm strength" or "leg strength" are problematic as well.
4. When people are grouped into strong and weak according to any number of criteria, the amount of variation within each group is far larger than the amount of variation between groups.
5. Strength is a social construct. Thus no one is inherently weak or strong. Scientifically, anthropologically, we are only human.
6. Scientists are rapidly starting to understand the illusory nature of strength, and one needs only to glance at any of the popular scientific periodicals to encounter refutations of this notion.
In on experiment, respondents from two different cultures were asked to lift a heavy object as much as they could. In one of the cultures, the respondents lifted the object higher. Furthermore, the manner in which the respondents attempted to lift the object depended on the culture. This shows that tests of strength cannot be considered culture-free and that there may be no such thing as a universal test of strength.
7. Indeed, to even ask "what is strength?" is to assume that there is a quality, or essence, of humans with essential, immutable qualities. Asking the question begins the process of reifying strength... (see page 22 here).
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For a serious statement of what the point of this was supposed to be, see this comment.