Oh, we all know what he meant: that famous SIXTH SENSE.
I suppose he often heard the expression but never saw it written down, or if he did see it written down he didn’t recognize it as that thing he had heard about. And I don’t condemn anyone who doesn’t pronounce it clearly enough for a child to picture all the letters: S-I-X-Th-Sense. Unless I’m doing some kind of diction demonstration, I don’t think I pronounce all the letters either.
As we know with Mondegreens and other such phenomena, when we hear something we don’t quite understand we often translate it into something that makes some sense to us (although not sixth sense). Clearly that’s what my student did here, and it does make sense, doesn’t it? Whether you think of that “sick sense” as being preternaturally perceptive, perversely suspicious, angst-ridden, or nauseated, it works pretty well to describe the feelings and insights that sometimes well up in the maternal brain.
That’s why I think my friend Philip will call this phrasing an eggcorn, a word substitution that has a kind of poetry to it. Only one word, but it really does say so much…
I myself could say more, but I leave it to your sixth sense to imagine what that could be!