The data doesn't say what you seem to think is obvious and what multiple people are telling you is that your assumptions do not fit every case.
You are being pretty rude to people telling you about their own experiences, it seems because it contradicts what you want to believe.
With single parents, most of the time they have no choice but to work, and they need flexible work. So they paint a particular picture that doesn't have much to do with what arrangements they might choose - their choices are constrained by circumstances.
It's fairly normal that in any sector, if you want a job with some kind of accommodation or other desirable element, be it flexibility, working from home, or something else - that you will trade that for lower pay. That's the reality for everyone. It absolutely hits single mums and makes things more difficult for them, but that is not the only kind of experience mothers have.
I could have gone back to work after my eldest child was born, in the same job. Which had pretty good flexibility, quite good pay, and even a childcare facility. I didn't want to because I wanted to take care of my kids, and I wanted to live rurally which meant more time commuting if I worked which imo is not great for a child, and I strongly prefered to home educate in the early years. And luckily because I was not a single mum, and my spouse was making a pretty good salary and our expenses were low, I was in a position to do what I actually wanted to do.
There are many, many mothers who are in a similar position, who want to take off more time, or return on a part time basis, or take a more flexible, but lower paid, job. And those things also go into the statistical analysis and affect the results.
You aren't going to convince people they are stupid and this does not happen because we know it happens, we can see it in front of us, and we know why we, and others we know, make these choices. Telling people they don't really understand our choices as well as you do, or are too foolish to understand the import, is pretty patronising, to say the least.