I think the point being made is this: boys are elements of the "set of boys". Asking the set of boys ("set" is singular) to "stand up" is not equivalent to asking the elements of the set (boys) to stand up. In this case, the elements (boys) of the set can stand up, walk, talk..., but the set of boys is, well, a set of boys: it contains the boys in the class.
It would be perfectly appropriate to ask the elements of the set of boys to stand up. Or better yet, to ask "if you are an element belonging to the set of boys, please stand," or even "if you're a member of the set of boys, please stand up." Those are different requests than asking the set of boys to stand up.
As aptly pointed out in comments above: In natural language, people often don't distinguish between a set and its contents. After Valentine's Day, e.g., I likely reported that "I ate an entire box of chocolates in two days!", and I certainly would not have meant that I actually ate the box containing the chocolates! So "real life examples" of the failure to distinguish between a set and its contents occur very frequently, and in real-life, making such a distinction can actually sound awkward, indeed!
I think in the example you quote, the author is trying to argue that "how sets are being taught in school" may be problematic, and in the case at hand, given that the request was made as part of an educational lesson about sets, subsets, and so on, the failure to distinguish between the "set of boys" and the "boys contained in the set" is seen as problematic, pedagogically speaking.