It's not you, it's me is a popular phrase used in the context of breaking-up, and is intended to ease the dumpee's feeling in the knowledge that it wasn't their fault, but because of a fault with the dumper.
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History
Merriam-Webster says that the phrase originated in newspaper articles which saw it being used in a sporting context where players would "either apologizing for or boasting about their abilities". But the phrase morphed into a romantic context from in the 1988 movie Casual Sex? where it was used in the middle of a seduction scene.
In 1989, a column written from the perspective of a sexually frustrated wife who uses the term "ran stateside in syndication", and in the same year an Australian comedian named Anthony Ackroyd deemed the line "unavoidably unoriginal".
The phrase was popularised by a 1993 episode of Seinfeld where George Costanza gets dumped by a woman who uses the phrase on him.
PsychologyToday offered an expanded version which reads: "'It's not you, it's me.' 'I hope we can still be friends'", which adds an element of friendzoning to the situation.
Explanation
The phrase's purpose it to ease a break-up and putting the onus on the person breaking up: "The person saying these words is taking responsibility for their inability to please you...It hurts them to hurt you." The phrase may be used as a vague all-encompassing, dismissive alternative "because the truth makes them feel shallow and embarrassed." An article in ThoughtCatalog used the phrase in terms of the "sad, honest truth [that] I don’t deserve a woman as good as she".
Reception
Merriam-Webster described it as a "much-reviled, often-used excuse". The Huffington Post described it as "overworked and clichéd". PsychologyToday argues that "Opening with "It's not you, it's me" is just going put your partner on the defensive from the start."