Any connector plugged into any socket is male. As such, the connection on the headphone side is male, and the receicing end (the BHA) has to be female.
While this is true for many types of connectors (plumbing, etc.), it's not so obvious for the world of electrical connectors.
For electrical, the gender of the connector is determined by the pins used in the connector - not the connector itself.
It's quite possible to plug a female XLR connector plug (designated as a plug by nature of its moveable position) into a male XLR socket (designated as a jack by nature of its fixed location).
In that regard, the statement that, "the connection on the headphone side is male, and the receicing end (the BHA) has to be female", is not a truism.
female jack

male jack

female plug

male plug

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