When you make a purchase, the extended warranty might cost somewhere between 10-20% for 2 or 3 years of extended warranty. Instead of giving the store another $10-$20 dollars on that $100.00 purchase for the extended warranty, I assume the risk and keep the money in my pocket. If the product lasts longer than the extended warranty, I consider that I have saved that money. Most of my products last longer than their warranty period, or even the extended warranty period. Over many purchases, I come out ahead on not buying extended warranties. If the product fails, and I have to buy a replacement, then I lose on that risk. That does not happen very often to me.
I suppose a person could actually set aside a pot of money saved from not buying those extended warranties. Then, if an item fails within that extended warranty period, replace an item from that pot of funds. Fortunately, I am in a position where I don't need to actually set aside money in a "warranty fund," but that is the idea of self-insuring.
I also use a related type of self-insuring my tools, and that is buying new tools on clearance just for their warranty period coverage. Some tools I need to have available at all times. For example...

I have many chainsaws of various sizes. I have 3 acres of wooded property and need to have a working chainsaw(s). When my old chainsaw out lived it's 5-year warranty last year, I bought a new chainsaw on clearance for about $90.00 with another 5-year standard warranty. That made more sense to me than paying about $50 for a 2-year extended warranty ($25 per year) on the previous chainsaw purchase. Now, I have 2 chainsaws that work, and one has a new 5-year warranty to cover my needs. I essentially paid less for a 5-year warranty ($18 per year) on a new chainsaw than what the store wanted to charge ($25 per year) for an extended warranty. Of course, the frugal part of that purchase was buying the new 5-year warrantied chainsaw at more than half-price clearance special deal.
I don't normally buy extra tools just for warranty period coverage, but with all the trees I have on my property, I need to have a working chainsaw(s) for cleanup after a storm, especially if a tree falls down and blocks my driveway.
Some tools will just wear out and need to be replaced. If you plan it right, it's often cheaper to buy a new tool with good warranties than paying extra for extended warranties on a purchase. Especially if you can buy the new tools on those holiday sales or clearance prices.