This answer is US-centric and is based on the fact that the US government implicitly subsidizes the 30-year fixed rate mortgage. Other countries and other financial systems have different trade-offs that make adjustable rate mortgages more common and more attractive compared to fixed rate mortgages.
Taking out an adjustable rate mortgage amounts to a bet that you'll sell the house before the fixed term expires or that rates will decrease and you'll be able to refinance at a lower rate or just enjoy lower rates when the rate adjusts. Broadly speaking, if rates drop, you win and pay less over the mortgage term. If rates rise, you lose and pay more over the mortgage term.
If you expect that you're going to be moving in less than 10 years, it makes perfect sense to get the slightly lower initial rate that an ARM has over a fixed rate mortgage. The median US homeowner stays in their home for 13 years but there are significant regional differences. And that tenure was much shorter just a few years ago. If you're reasonably confident that you'll want to move before the rate resets, an ARM is an attractive choice because the rate will generally be a bit below the fixed rate.
If you expect that interest rates are going to decline, an ARM is advantageous as well. You can always refinance to the new, lower rate assuming you maintain your creditworthiness and your home maintains its value (of course, you can always refinance your fixed-rate mortgage as well, it's just that fixed rate mortgages will have a slightly higher rate than ARMs). And if you don't refinance, your rate will decline when your mortgage interest rate adjusts.
On the other hand, if interest rates increase, your payments may increase substantially. Although rates have gone up quite a bit in the last year, they're still at historically very low rates. Looking at the historical record, there is a lot more room for rates to increase than to decrease. And if rates go up, you may find that your payments after the first 10 years go up dramatically. Your ARM will specify a cap that your rate can't increase above but that's going to be several percentage points above what the initial interest rate is. If you're looking at, say, a 4.5% ARM right now, your cap might be 9%. If rates go up (and rates have been above 9% many times throughout history), would you be able to make the mortgage payment at a 9% rate? That would be a struggle for a lot of people.
For most people in the US, an ARM is a pretty poor bet. If you win, you do slightly better by getting a lower rate for whatever time you have the ARM. That's probably worth thousands of dollars for most transactions but not tens of thousands of dollars. If you lose, though, your losses can be far more than a few thousand dollars. If interest rates hit your cap, you could be looking at monthly payments that jump by $1,000 or more when your fixed rate term expires and continue at that value for the remaining years of your mortgage. There will be a cap on how much the rate can jump at each 6 month adjustment so it would likely take a couple of years to hit your overall cap but then you'd be stuck paying that higher amount for the remaining 16 or 17 years of your mortgage term (assuming a 30 year mortgage).
