NC for this as I expect some anger.
I agree that it is shit that many men don't pay CM at all, many don't pay enough, women have to take on the lion's share of costs, work etc. Many men shirk their duties. I also agree that OP's ex should pay.
In terms of why the men in the Facebook group might feel how they do, it isn't hard to imagine how - for some men on low incomes and minimum wage - CM payments are a large burden. On separating, a man might need to leave the family home with nothing.
Renting a one bed flat in my area (not SE or London) costs around £800 per month. If the man is on minimum wage (around £1550 per month full time) and has 2 children then he would need to pay £250 per month CMS assuming he doesn't pay into a pension and has the kids 0 nights due to only living in a one bed flat.
He would be left with £450 for the month after rent and child maintenance. It isn't hard to see how this would be financially taxing when he also needs to pay council tax, food and energy. Let alone basic travel, days out with the kids. Then nice to haves like dentist, clothes, birthday + Xmas gifts, pension. Let alone having spare money for treats or saving for an emergency.
If the father has low education, getting a better job might not be that easy. In some roles over-time isnt available. Men in the situation i have described are real and do exist. Yes, he could get a second job, or rent a room instead of a flat.
Additional bitterness from the men is likely to come because the resident parent can claim benefits so 'will be OK'. If she has a low wage she will get universal credit to help with rent and the child costs, council tax benefit. Basically, I'm saying, it isn't that shocking that opinions like you have seen on the Facebook page exist.
However, I also know that not all men paying CMS are in the position I described. And there are many women and children living in poverty.