For a more detailed answer, a "man calling himself a woman" typically refers to a trans woman. Being transgender is a fairly well understood condition where the person is what they say they are. There are several different scientific studies that compare different parts of the brain that are known to be sexually dimorphic, and in trans people, pre or post hormones, their brains tend to match their claimed, rather than their assigned gender.
Further reading.
For context, and why your comment was in particularly bad taste, there is a common joke on the internet where people claim to "identify as an attack helicopter". Innocent of that particular joke or not, anyone with a sense of history on the internet would almost certainly make that connection.