Apparently there have been many question regarding tire width to wheel width correlation so, here is a sort of technical response.
While tires can and do fit a wheel width range (i.e. a 225/45-17 range is 7" - 9") there are serious issues going outside that range
here's poorly executed picture to base the conversation on
in figure "A"
the tire size is properly mated to the wheel width. That type of setup would allow the tire to achieve the best possible control of the contact patch and offer the most support for the weight of the vehicle.
in figure "B"
the tire is too narrow for the wheel so, as you can clearly see the sidewalls are not anywhere close to verticle which would cause the tire to not have the proper load capacity or control of the contact patch thus reducing it's ability to perform it's job and creating more heat.
in figure "C"
the tire is way too wide for the wheel and just as in figure "B" the load capacity is adversely effected as well as contact patch control because of the excessive sidewall roll over.
in both figure "B" and "C" the sidewall of the tires are under extreme stress which can cause several things to happen.
just to mention a few:
#1.) catastrophic sidewall failure due to load issues
#2.) complete tire failure due to excessive heat being generated by additional flex and/or roll of the sidewall
#3.) adversely effected handling since the sidewalls can not control the contact area properly
#4.) beaking of the tire bead area under extreme cornering causing immediate loss of air pressure and vehicular control.
I mentioned load capacity as a very important issue in my previous statements so, let's consider the idea of running a capacity that is too low .... what happens:
the tire is put into a condition where it can support the car at a static rest point but, when driven aggressively the sidewalls are so over worked they can not properly control the contact patch of the tire allowing for excessive sidewall roll-over, irregular wear tread block and contact patch flex which robs the tires performance ability and grip. also the added flexing of the tire will increase the heat it generates which can make a tire feel really slippery .... and if you can't utilize the power you're making nothing else matters afterall the tires are the only item on your car touching the road ....
A good way to understand this is: let's say I just put a 100lb. back pack on you .... you can stand there for quite a while (that's your car sitting in a parking lot) now go run up and down some stairs with that back pack .... that's normal driving and you can't do that very well, nearly as fast or for very long before your legs give out .... after you've recovered enough to walk (let the car rest once you arrive at the venue for your autoX), take a 500 meter sprint through deep sand, that's your autoX and you will most likely not make it to the finish without falling atleast once if you can finish at all.