The fact that something's socially constructed doesn't mean that it doesn't exist, or that it doesn't arise from a biological predisposition. Language, for instance, is socially constructed in its specifics - it's perhaps the ultimate cultural artifact - but our brains are naturally predisposed to learn it, create it, and work with it within a very particular non-arbitrary set of rules.
The specifics of gender performance and identity are arguably socially constructed. That doesn't mean gender doesn't exist, or that there's no biological reason for an individual human to identify with one side or the other of a binary gender system differentiated primarily by visible physical sex. As far as we know, all human societies are structured in more or less this way.
And humans are highly social animals that can't be studied effectively in isolation from our social environment. A human who isn't socialized around other humans isn't a healthy individual, and is most certainly not existing in their 'default' natural state.