This surprised me because I think I remember reading Buffett says re-insurance is the backstay of his profit, and investment.

From what I understand, insurance companies were/are his cash cows so to speak. The simplified business model of an insurance company is to take the money customers pay for the insurance and invest it safely enough that you can cover the sum of payouts required and make an extra profit. Now in theory this is profitable without high returns from that investment because the sum of payouts is less than the sum of money collected if your risk models are correct. But if you assume that you are above average in investing (which Buffet assumes) then it becomes even better to buy these companies because you are the one who gets to invest said money.