You always fit the best tires on the rear. Why? They don't motor*, don't steer and barely brake - why can't rear wheels just be casters?
The rear tires are your rudder
They keep your car from spinning out. To be technical, they provide stability in yaw, and they don't steer, so vertical stabilizer is more correct. Ever seen those on the front of an airplane? Nope, and for good reason!
Driving a curve (and some other things) put sideways force on every tire. Here's the key question: In poor traction, will your front or rear tires break away first?
If your front tires break first, your car will seek to go in a straight line. (understeer). As it gets near breakaway, you'll notice - the steering will be less responsive. If you are properly trained, you will "turn into the skid" (align the steer wheels with the direction you are actually going). Why? Wheels have best sideways traction when rolling straight - when cocked at an angle, traction is much worse. By aligning wheels with the skid, you get maximum traction and soon recover control. (and of course this will correct the rear problem too.)
If your rear tires break first, there is nothing you can do about it. You can't steer your rear wheels into the skid. The increasing angle makes traction even worse - a vicious cycle, which is why a spin-out is hard to stop! I've spun 360 on a tight cloverleaf freeway on-ramp going 25 mph in simple rain. That's when I grokked the "rudder" thing, and put my best tires on the rear.
Best tires go on the rear because you want the rear to break away last.
The rudder is their main thing
Of course they support the weight of the car, but in front engine cars, 60% of your weight is on the front. When you brake hard, it shifts the weight even more forward! So most of the braking is done by the front.
And the vast majority of cars are front-drive, so the rear wheels don't even provide power. They might as well be casters, except for the rudder thing!
Sideload, steering and power/braking all tax the same traction
A tire has a finite amount of traction. Sideload, steering, and power/braking all "dip out of that same pool" of traction. If all of them together add up to more traction than available, the wheel must slip!
On the front wheels, that's much more manageable - because you control power (on a front drive car), braking and steering. You can back off any of those and put that traction back in the pool for something else to use. You can't do that with the rears, unless it's a rear-drive car and you can lift off the throttle.
In fact, in a rear-drive car, if you punch the throttle hard, you can use up all the traction and cause sideslip. It's very easy to over-do it and spin out entirely... but done right, it is drifting or a bootlegger's turn, and swings the rear around right where you want it.
* Presuming FWD cars, which are the vast majority of cars on the road today. I cover RWD cars at length in the non-TLDR section, and frankly, RWD drivers tend to be knowledgeable and understand their car is an exception, and don't need this explained to them.