“It's not you, it's me” has become shorthand for a cop-out, and often it is one — a vague phrase deployed to avoid saying something more specific and more true. But the line persists in the culture because it sometimes describes a real situation: a breakup that genuinely isn't caused by anything the other person did wrong.
Not every ending has a villain. Sometimes someone is dealing with something in themselves — not being ready for commitment, working through unresolved issues from a previous relationship, or simply not having the emotional bandwidth a partnership requires — that has nothing to do with their partner's behavior. In those cases, insisting on finding a fault in the other person, just to have a more “concrete” reason, would actually be less honest.
The problem isn't the sentiment; it's that the phrase has become a reflexive script, used even when it isn't true, which has trained people to hear it as a lie by default. If it genuinely applies to your situation, it helps to add specificity that proves you mean it: “I'm not in a place to give anyone what they deserve right now, and that's about where I am, not what you've done.”
Said with real specificity, instead of as a reflex, the sentiment behind the cliché still holds up. It's the vagueness that damaged its reputation, not the idea itself.