Why am I afraid of tiny spiders?

Likely that you have simply brainwashed yourself into fearing small spiders. I know people that keep tarantulas for pets, yet scared of small house spiders, so this is not uncommon.

Smaller spiders can easily hide, and often hard to catch without hurting them.

The smaller spiders are typically 'totally harmless', I usually just ignore them or put them out of harms way. Never found them to be a nuisance at all.

I can't solve your hatred(that is your call) but you might try catching a small spider in a cup, take it outside, dump it in your hand, and let it crawl on your hands before dropping it in some shrub, you will see they are really inoffensive little critters.

Because they grow up to be large ones?

I HATE ALL SPIDERS