Wait a moment. The stereotypical unstable oil is alpha-linolenic acid, which seems to be generally regarded as quite healthy. Certainly oxidized ALA is disgusting (keep those flax seeds in the freezer!), but I’ve never heard of omega-3 fatty acids leading to fragile cells.
ALA is very unstable as oils go. It’s an omega-3 fatty acid. It’s generally regarded as healthy. The claim that unstable oils are somehow bad for you because they are unstable in your body seems entirely unsupported.
Certainly flaxseed oil is a terrible cooking oil unless you are trying to make furniture [0], but that’s a very different claim.
[0] You can also use flaxseed oil to produce a beautiful but mostly useless seasoning on cast iron. But the inside of your body is not made of hot iron, and the reactions that occur on a skillet don’t seem particularly relevant to what happens if you eat the oil.