Almost any saying that starts with 'you will always...' or similar is bullshit.
There is a saying that the only inevitable things in life are death and taxes, which I find pretty hard to disagree with (even those who get out of paying most types of tax surely still end up paying some at some point, even if it's just like VAT on a purchase. Perhaps some people somewhere in the world live in a sufficiently isolated or underground way to avoid it, although I bet even communities that don't pay tax in a monetary way to a formal government still have a network of obligations that people can't get out of and are functionally similar to a tax... I disgress.)
But other than that...
I think the saying you refer to is useful to some people in some contexts. For example it can be so easy to be consumed with a lot of hurt and anger after a breakup, and some people end up understandably struggling to coparent when those feelings are so powerful. There are probably some people for whom focusing on some of their ex's positives and on tu contribution they've made to the creation of shared children (even if literally only the biological one) is a useful corrective and a helpful perspective.
But not everyone loves the father / mother of their children to begin with. People who are in love fall out of it. And as you say, there are certain types of situation involving abuse for example where it might be completely underandsble and even necessary for a person's survival and for their children's safety to deliberately try to shut off any lingering loving feelings, especially if they keep pulling you back together.
So yeah, absolute rubbish to always apply it. Most sayings and 'rules' have some utility to some people, which is presumably why someone bothered to think of them and others have bothered to repeat them, but that doesn't make them useful to everyone, and it certainly doesn't make them true!
(Edit: I also wonder whether some people say this sort of thing to justify mistreating their new partners whilst remaining emotionally overinvolved with exes with whom they have children, or refusing to set consistent boundaries with exes. I reckon that's a darker potential use of the phrase.)