(This rapidly becomes clear when teaching English as a second language!)

Even better than learning a second language is teaching one. The to in the English infinitival form is related to the preposition to. That much can be ascertained by parallel constructions in other Germanic languages and in some Romance ones.

I once listened to a historical linguist give a good lecture on the particles of a language: all those little parts of speech left overs like preopositions, adverbs, verbal particles, etc. The preposition problem is English was exacerbated by the lose of case in the nominal paradigms ...

Ceci n'est pas un seing.