I'm fairly sure a big part of the driver for the imbalance in education is that being a teacher is one of the only ways, other than being a full-time employee (not contractor) some place like Google, to access European-like levels of parental leave, plus European-like levels of time-off, generally, which is also hugely valuable when you have kids, while also being a career in which leaving multiple times for months at a time to have kids (if you time it well with Summer, or hit up FMLA time) is minimally disruptive to one's career growth, which is unusual for non-very-rare-and-hard-to-get jobs. Plus, and this isn't to be under-appreciated, teachers are in demand everywhere, so one can gain all the above and move to (for example) let your spouse chase higher wages at a less-family-friendly job (nursing is similarly friendly in that demanded-everywhere way, and go figure, nursing is dominated by women, too).
Relatedly, teaching is also one of the most single-parenting-friendly jobs around. The pay may not be great, but you're off (more or less) when your kids are, it's stable, and it comes with benefits. Retirement, even! It may also let you do things like get a job in a good school district, while living in a worse district (cheaper housing), but send your kids to the better district you work in, which can make a huge difference if you're on a single income.
For younger grades in particular, I think it's all of the above, plus a combination of simple interest-factor, and of men fearing (not unjustly) that any interest in or affinity for young kids (who aren't relatives) will make them look extremely creepy.
In a Swedish study the term they used for the teacher profession was a "leaky pipe". The first year at university the teacher program is only somewhat gender segregated, but for every year that goes men either quit or refocus towards a specialty with more men. Once graduate, each year as an employed teacher the segregation rate increases with men either quitting or switching to a specialty like after-school sport.
The number 1 cause as highlighted by that study: culture fit and not feeling accepted.
* Preschool and kindergarten teachers 98.8% female
* Elementary and middle school teachers 79.6% female
* Secondary school teachers 58.8% female
* Postsecondary teachers 51.1% female
There's clearly a lot more going on here.
That makes sense, but personally I think you should still focus on the "smaller issues" instead of just looking at the most extremes. People who are "a little aspy" may have similar biological causes as severe autism, but their social situations are much different. People with Aspergers may just require some minor accommodation to live their lives, but people with Autism may require a lot of care. The causes can be similar while the scale drastically changes the type of response.
"Driver/sales workers and truck drivers": 3.4m, 92.2% male.
92% of veterinarians are female
98.8% (!) of preschool and kindergarten teachers are female
If you want to understand gender imbalance in employment, these are the obvious places to start.