In Situation 2 you have pledged your house against the 100K loan, the fact that an LLC is involved is immaterial. There is nothing that can protect you when you want to take equity out of your house and you lose all of the money.
Situation 3, you borrow money to start your business, it takes off, you pay it back and your business continues to grow. Later you are sued and lose a 10M lawsuit wiping out all of the assets in your business and then some. If you have a corporation your personal assets are normally protected from this loss. Alternatively your large and growing business is struck by a meteorite (which can come in many forms) that wipes out all of your assets but leaves you with the liabilities. If you are incorporated winding down the business normally doesn't affect your personal assets.
(I know you're not a lawyer, but am trying to get an impression for this). Say instead of $10M I get sued for $50K. In the $10M case I clearly can't pay that but in the $50K case, I might be able to sell my car, move into a cheaper house, etc, in order to pay it. Am I protected in both cases? What about $10K? At what point is it "OK, you can't pay this, go declare bankruptcy so you get to keep your personal assets"?
If you lose a lawsuit (or are hit by some flavor of meteor) the business has to pay for it to be able to continue. All that creating a corporation does is to clearly separate what are personal assets from corporate assets.
It may be easier to visualize if you imagine there are several shareholders. Each would want it clear what were the company's assets and what were their personal assets (in addition to their share of the company).
Look at it this way, you buy 100 shares of GM which subsequently goes bankrupt. Your shares may be worthless but GM's creditors cannot come after you as a shareholder for more than the equity that you contributed (the money you paid for your now worthless shares).
Situation 3, you borrow money to start your business, it takes off, you pay it back and your business continues to grow. Later you are sued and lose a 10M lawsuit wiping out all of the assets in your business and then some. If you have a corporation your personal assets are normally protected from this loss. Alternatively your large and growing business is struck by a meteorite (which can come in many forms) that wipes out all of your assets but leaves you with the liabilities. If you are incorporated winding down the business normally doesn't affect your personal assets.