I think the answer is actually somewhat political, but there are also some practical issues.
I can't claim to know for sure what is the path one must take before becoming a tennis coach, but I'm assuming many started off by being hitting partners, who are predominantly men. You need early tour exposure for that kind of thing and men's tennis is far more flesh out in that regard. Given that being a former tennis great is not always the pathway to coaching, and many retired players on the women's side aren't interested, I think this leads to an uphill struggle for an aspiring coach.
I think many women simply aren't too interested in being on tour with the players from a societal standpoint. This is pure conjecture, but being on tour + strict travel schedules don't mesh well with raising children for instance, if someone is a mom or hopes to become one.
And finally, at the risk of sounding woke, I do think there's the usual stereotypes as to who is taken more seriously than others, who gets opportunities, who is seen as having better pedigree or perceived to be more capable, and I have a feeling men benefit on that front.
