Some places just have "social dancing" classes, which is a different thing each week, but they might require you bring a partner, so look into it.
If you're from the US, or less commonly outside of the US, line dancing is a non-partner dance, so a group dance. One of my best friends does it and he loves it. Again don't need to be good to start.
When the balance gets skewed too hard one way or another, lead/follow becomes less sex-discriminated. Which usually means that women lead too. But in the past few years it's become much more acceptable for men to follow as well, at least in some contexts.
There are places where men dancing is gay-ish and that deters them. That's an easy answer, but it's not enough because very progressive countries don't do much better on this, by my experience.
I would agree learning to follow in the very beginning can be easier, so that sounds like maybe men don't remain because their job is harder, but I wouldn't agree with this explanation because I observe fewer men showing up for beginner classes, when they don't know their job might is harder (whether or not it actually is).
Maybe men are more asocial on average? I'd be willing to believe that, especially in these times.
A comment above yours comments that this isn't true in Turkey, Buenos Aires, and I would add Paris to this list from experience, and then there's the entire continent of Africa we haven't mentioned and I can't really comment on, but what those places have in common is a cultural presence of dance, often a deep connection to dance where families dance together, maybe mom dances when she's cooking, dance isn't something you pick up as an exotic hobby, it's just that thing everyone does, and maybe you decide to do it a bit more than others.
Every culture with a lot of cultural dance presence would have a different view on this, I suspect.
While we all have all of the sides, for such a person, other sides are atrophied from under-utilization, while mind is hyper-trophied from overuse for for things it is not so good at. The primary obstacle for a person like that is to start developing the atrophied sides.
If this is the case, the best way to start is with the simplest possible partner dance, because mind-oriented people naturally approach learning complex body movements through mind, which is exactly the opposite you need to be doing.
So something where steps are one step per beat, like Swedish bugg.
muscles store physical energy in the form of tension, if you can create a bit of tension [here] then smoothly transfer it [there] you are "dancing".
how it looks to an observer is irrelevant. stretch this game enough on every dimension and it will eventually start to look [positive valence] to observers