It was just an example.
When a lot of people say gender is a social construct, they tend to really mean gender roles. As in, the idea of women being the home maker is a social construct. The fact that society deems men who cry as weak is a social construct. The idea that women can't be warriors is also a social construct. But gender roles are not gender. Gender is a representation of identity. It is one of the core parts of identity. You can say it was socially constructed, but people tend to have a preference for the company of their own gender. If gender is a social construct how do you propose one undoes this construct? Men tend to act a certain way because of testosterone. A lot of gender is related to biology. If gender is a social construct, it must also be able to be deconstructed. Race can be deconstructed because despite our differences, we are all human, and those differences are superficial at most. But a man way different than a woman. And although gender roles can very much be social constructs, they're also usually based on element of biology. Such as the fact that men tend to be warriors more than women because they're usually taller and stronger. The way a man acts is often determined by his hormones created in his testicles. This doesn't mean women can't be warriors, but a man is far more likely to take up that role simply due to biology. Or that women tend to be more doting on children than men. Trans people have been shown to have brains more similar to the sex they identify as, showing that gender is innate and biological.
Essentially, people who argue gender is a social construct rightly examine that much of society pidgeonholes people into boxes due to the times of ever changing gender expression. But this does not mean gender itself is a construct. You can have one without throwing the baby out along with the entire bathtub.
Gender is a social construct is an argument often propagated by radical feminists who hope to prove that both man and woman are the same. They aren't the same.
