I know my gender is female because I have zero desire to present as male and to integrate myself into society as a man. My biological sex and my gender identity align. My FTM trans friend, however, would feel differently. He was born biologically female, as the other comment explained, but feels a disconnect between his body and his identity. When he looks into the mirror, he is made uncomfortable or distressed by his feminine body shape. This is called gender dysphoria and is required to be transgender.
Gender is not a social construct. If it was, then trans people would be invalid. The people who say that gender is a social construct often say it with positive intentions, trying to say that people are free to express themselves however they wish. However, they probably mean that gender roles are a social construct, which is accurate. Different cultures and societies vary in gender roles. For example, in the Western world, it has for a long time been expected of a woman to stay at home and look after children while her husband works. However, the Mosuo, a famously matriarchal ethnic group from China, would disagree. The role of the woman there is to do the housework and bring in the money, whereas the man is expected to raise his sister's children and build the house. Some would say that the Mosuo man has no responsibility at all because he doesn't work and he rests all day.