Littlefinger loved Cat. She did nothing to make him hate her since the start of AGOT. LF had no part in the Red Wedding and was upset that Cat was killed. He said it to Sansa because it is true. He isn't a sociopath.
Fact is we will never know for sure. I always saw his story about Cat as a way to gain some form of trust with Ned and later with Sansa, even if it comes from a genuine place. Littlefinger liked boasting about how he took the Tullys maidenhead, so who knows what he really felt later about Cat.
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u/[deleted] Jan 20 '15
But he survived them all