To provide a reverse data point, I’ve had female travel companions come first on reservations plenty of times, when they were ahead of me in the alphabet lottery. Especially fun the first time it happened, on a BA Holidays booking, where the hotel insisted there was no reservation under my name (despite being the lead pax) when we arrived tired and exhausted at 1am. Only eventually did they find one... under my partner’s name.
So, Occam’s razor on this occasion. That’s not to say BA doesn’t provide genuine examples of sexism - look no further than that pathetic “safety” video and how the “director” talks to one woman in particular.