Sure.

> Why do you refinance if rates go up? Surely the point is that if rates go up you've locked in a better rate

You don't have to, but you can choose to either (a) keep the same rate and owe the same amount, or (b) get the new (higher) rate and owe less.

> How does half your debt disappear if rates go up?

It doesn't exactly. However, the market value of your mortgage loan halves if the rate doubles (roughly). This means you can:

1. Take out a loan for half the original amount, at double the interest rate

2. Buy back your original loan

3. Destroy the original loan (which is fine since you are both creditor and debtor for that loan)

This leaves you with the loan taken in step 1.

To understand why it works this way it's instructive to think of a loan as an exchange of wealth for income. One party has some savings (wealth) and would like to exchange it for an income (e.g. to pay recurring expenses). Another party has an income and would like to trade it for wealth (e.g. to buy a house). Viewing a loan in this way, the interest rate is nothing more than the current price of a certain income stream (measured in percent per year).

For example, let's assume that the current market price for an income of $2 per year is $100. This is equivalent to an interest rate of 2% per year. I have $100 that I'm willing to part with for an income of $2 per year, and you have an income of at least $2 per year that you're willing to sell for $100. We make the deal. Now, the day after we shake hands to make the deal, the current market price for an income of $2 per year falls to $50. This is equivalent to a doubling of the interest rate (from 2% per year to 4% per year). I still have the income of $2 per year that I paid $100 for yesterday, but if I want to sell this to someone else I can only get $50 for it. And if you were to ask me to buy back the loan for $50 I would have nothing against that, since I could go out immediately after and buy the same $2/year income for those $50.

The rates usually don't go up because the lender got greedy and felt like screwing you harder. If the mortgage rate doubles, that's because your money is now worth less than it used to be. This also likely means that your income is going to grow soon enough, so you wouldn't have much trouble repaying your loan. While your remaining loan is still nominally $N, if you took a loan today for the remaining part using the paid-off equity as collateral, you could likely get twice as much and the lender would proceed accordingly.

I wonder if the way I use "homeowner" differently than the phrase "own their home" is particular to me. I wouldn't say someone with a mostly unpaid mortgage "owns their home" even though they are a homeowner.

It is "their house" and things like that also, but I hesitate to directly say that they own it.

The differences are apparent in the US as well. The bank is making offers to a broad population without knowing their life plans. The borrower has a better idea of their individual life plans. I was buying my “lifetime home” 15 years ago and so took a fixed rate. When I first refinanced, I still had the same plans. When I second refinanced, I still had the same plans.

Even among fixed rate products, there’s an option to buy down the fixed rate. Those usually have a point in the future where all choices are about the same, shorter favoring not paying points and long favoring buying discount points (this crossover point varies over time by current and expected rates, but is in the 4-8 year range typically).

In the US, you can refinance your loans. Essentially taking out a new loan to pay off your old mortgage. The new loan has the new market interest rate. In the US, you’re typically allowed to pay off additional principal without any penalty, so you can end a loan by paying off the outstanding principal without needing the pay the remainder of the interest on the loan.