The single mums I know have told me that there is just so much dishonesty in the men they have met. Most of them say whatever is needed to get into bed with them. Or they think that these women should be happy to cook and entertain the man's own DC during 'his time' so he can just sit back and watch telly. Or they're cocklodgers or men who feel a single mum should thank their lucky stars that any man would 'take it all on' and so cater to them.
Even the men who have actually wanted relationships end up resenting the fact the their time is limited and that single mums aren't truly free to come and go because of child responsibilities. Or they say that they're fine with kids, but then decide they don't want the responsibilities that come with them.
I will say that most of the single women I know who've found happiness again have met their new partners through work, friends, or other social situations (hobbies, church, etc) rather than OLD. I think it's because they had friends to 'vet' the man or they've had a chance to get to know them a bit in person.
I think many women who say 'never again' are survivors of abusive men or men who expected them to do everything whilst he never gave up the bachelor life-style of beers with mates, hobbies on weekends. In other words, neglect of the marital relationship. No wonder they don't want to get involved with anyone!
But there are many of us who are in happy long marriages who also say 'never again'. I'm one of them. My DH isn't perfect by a long shot, but he's a good man with good values, and we've been happy together for over 35 years. As my mum used to say when people asked her why she had no interest in dating after my dad died "Why should I settle for hamburger when I'm used to dining on steak".