Why you should only buy what your car needs. If your car calls for 87 octane gas, that means it’s going to compress that air/fuel mix to a point where 87 won’t ignite on its own. If you pay more and add in 89, you get no benefit because it’ll only compress that mix to the 87 level. You get no added benefit because your engine can’t take advantage of the higher compression ratio.
Why you shouldn’t skimp and buy a lower octane than required. Your engine operates most efficiently when that air/fuel mix explodes when it’s supposed to explode. The whole timing of the engine is fouled up when it explodes early and that’s what happens if you put regular gas into an engine designed with premium in mind. When 87 gas is compressed to 91 levels, it’ll explode prematurely and foul up the timing of the engine (this is known as “knocking”).
Why people think higher octane is better. Because it is better! If all other specs are kept equal, an engine with a higher compression ratio will have greater horsepower. However, you need an engine that is operating with the higher compression ratio. If you have an engine compressing for an 87 octane fuel and you put in 91, nothing changes except you’re a little bit poorer.