Agreed.
I often cycle a short distance to work. I tend to wear trousers for practical reasons anyway, and fortunately my ride to work is downhill so little effort compared to the ride home where I have no pressure to look or become professionally presentable upon arrival.
I have a female colleague who sometimes uses her e-bike, but overall cycling amongst staff is low and I'm not aware of other regular staff cyclists.
The interesting bit is the ratio of male: female students who cycle. I can only think of one girl who I see cycling regularly (and the only "feminine" colourway bike parked up), and she has an older brother who cycles in, so there is a role model presenting cycling as a normal form of transport. The rest of the regular cyclists are all male. The cycle racks are well filled, and we have a local catchment on relatively accessible routes.
While it's superficial, the impact of cycling on clothing choices (within the uniform) and appearance will be a barrier to many of the girls using cycling as transport. There isn't provision to change and freshen up and this would put them on site too early and raise supervision issues. There is more time and higher expectations in meeting feminised beauty standards. Personally a washed face and brushed, tied-up hair is good enough for me, but many females opt to engage to a higher effort and there can be a lot of social pressure on young females, and there isn't a template of girls cycling for transport being set in (our) school. Girls are also more likely to walk in larger groups as social activity whereas cycling is less social while on the move. There will also be a personal safety angle in the equation.
Childcare is no longer a significant issue to me, and my teenage DCs either get taken by DH or bus. However the days of childcare ruled out options such as cycling and buses for me because the increased travel time didn't fit for doing nursery/ school drop-offs and getting to work in the window between childcare opening times and work start time, and it was tight enough by car. At that point, their childcare fitted with my commute better than DH's, and now they go to school in DH's direction. While cargo bikes solve a capacity issue of transporting young children, I would not want to use them on a hilly, busy 40-50mph route for the rest of that journey after drop-off (my workplace has changed)
The tweet is badly written and presents those two issues in a trivial way. There are also other issues such as culture/ role modelling and personal safety, but it doesn't mean that the two issues raised are not relevant.