Business relationships take place within a business context, email, meetings etc where both parties are pretty clear on intent.
She messaged him on Facebook, that's not a professional environment, it's social. He took it as such, his messages weren't inappropriate. Labelling it as 'sexism' is a little much, it's normal human interaction.
She messaged him on Facebook after finding him through a Facebook group dedicated to entrepreneurship. If we grant that facebook is a more casual environment, for the sake of argument, his line of questioning should have ended at "are you single"! I don't see how her intent could have been more clear.
Furthermore the Facebook platform (lets include Instagram, Whatsapp, etc) has become an "everything" platform for many individuals both young and old. Family, news, everything is on there. In the absence of clear intent the expected behavior should be not to make such drastic assumptions as sexual interest...
Who seriously jumps from business into asking, in rapid succession, a persons age, relationship status and details about sexual orientation? These are personal questions: they don't correlate to success in any meaningful way and frankly, are none of anyone else's concern.
She messaged him on Facebook, that's not a professional environment, it's social. He took it as such, his messages weren't inappropriate. Labelling it as 'sexism' is a little much, it's normal human interaction.