The difference between them is that אותי is a direct object (just saying "him") לי is indirect (when you would add a preposition in English like" to him", "at him" etc.)
In English, the verb "to answer" is transitive (takes a direct object) so it's "answer him". In Hebrew לענות is intransitive (takes an indirect object) with the preposition "ל-" so it's לענות לי.
Verbs have a somewhat idiomatic relationship with their prepositions, it doesn't translate directly.
Yes, there's some linguistic "logic" we absorve more by using them (hearing, writing etc.) than studying the grammar. That's how kids learn, and how we can get it faster.
But, after get the languages in a subliminar way, it is very important to understand their grammar, to improve your understanding and, naturally, to can express yourself better.
Most of the school time, we're too young to value this grammar studies properly, and so we lost many opportunities to improve the learning of our own language. But, when we the interest to learn another language we finally feel that calling, showing us we need it. By trying to learn the other languages somehow we often discover our own language in a way we didn't ever experience.