It's an old joke, but one I still hear occasionally when men find out I do half the childcare in our family: "Are any of the mums at the school hot?"
When my two were very small and I used to go to new baby clubs, I'd be asked if I got to see a lot of boobs.
Mostly I'd just laugh this stuff off. Sometimes, I'd even laugh along with it. But this week, I got to feel first hand how difficult it is to shake the sexual element when it comes to relationships between men who are hands-on in childcare, and the mums who dominate the world of children and school.
There are two girls in my four-year-old daughter's class who, like my daughter, also have younger brothers. As the girls have got to know each other in class, I've been thinking for a while how good it would be to get the boys together so they can play together too.
For a couple of weeks I've been holding back. When I plucked up the courage to approach their mums outside the school gate this week, there was a nervous quiver in my voice.
My fear was not these women wouldn't see the logic of having our boys play together and refuse. Rather it was that my invitation - for two women to come back to my house, while my wife wasn't there - might be taken as some kind of sexual advance.
The mums said it was a good idea, though did I detect a slight nervousness in their reply too? Later in the week I wanted to confirm, but held back from approaching again in case they through I was being just a little too keen. I certainly didn't feel able to ask them for their mobile numbers, so we could settle the details.
It was like being a teenager again, too afraid to talk to the girls in case I got rejected. (Only back when I was a teenager, I really did have other things on my mind.)
In the end, my wife agreed to be around for the start of the play date, so the boy-girl factor didn't feel so apparent.
This theme is one familiar to other involved parents I interviewed for my book on shared parenting, Men Can Do It.
As one full-time stay-at-home dad put it: "I can't walk up to a woman and introduce myself, it would feel like a come on. But women do it all the time with each other. I wouldn't make an arrangement to go round a woman's house if the husband was at work. You just can't get the sexual element out of it."
And it goes deeper. My daughter's head-teacher recently put out a call for parents to come and run the after-school book club, which being an author myself would have been right up my street. Except the advert described the "very eager group of girls" awaiting a new volunteer.
I decided it might be best for me to volunteer with the more gender mixed gardening club instead, lest someone get the wrong impression.
Perhaps I am being oversensitive. But if a hands-on involved father like myself is worried about the perceived sexualisation of my relationships at school, surely others must at least be thinking along the same lines?
Afraid that my involvement with mums, or with girls at the school, will be regarded as sexually motivated, it seems easier to take the option of not getting involved at all.
That's incredibly sad. It's no wonder one in four primary schools have no male teachers, and that there are just 48 men working in state funded pre-schools and nurseries UK wide.
How to break the deadlock?
I'm convinced the solution is for men to go ahead and ask for the playdates, and volunteer for the book club, whether it is uncomfortable for us or not.
For too long, men have excused themselves from the woman-dominated world of parenting and school, making any number of excuses for not being involved: work, social stereotypes, not being good at it, the perception of a sexual element.
That means these areas stay woman-dominated, and the vicious cycle continues.
Being visible and active as an involved father at school, even if it makes us a bit nervous or we worry that others will get the wrong impression, is the only way to demonstrate we can be trusted around children - yes, even groups of girls - and that any relationships we build with the mums of our children's friends can be purely friendly.
We have to demonstrate our competency with children. We have to show we can be interesting, engaged and knowledgable people for other parents - men and women - to talk to.
The more visible and active fathers become, the easier it will become for other fathers to overcome these barriers too.
It may be a little uncomfortable at the start, but if we want our children to benefit, fathers have to make the first move.