With verbs such as "cacher quelque chose à quelqu'un" or "éviter quelque chose à quelqu'un", we can see the preposition "à". But from my knowledge of French, this preposition very often has the meaning "towards". But in cases of "cacher" and "éviter" it means "from" (to hide something "from something").
Is there any reason of why it happens (perhaps historical one)? How should I think about it?
When used with persons, à usually marks the beneficiary/recipient (a dative of sorts):
Baptiste a fait une fleur à Christine.
Paul a donné du pain à Marie.
Beneficiary is to be understood as recipient, the result might not be an actual benefit from his standpoint as in your first context.
If you try to apply one language's logic to another, you will indeed conclude such things. But be sure that for a French native speaker learning English, the English form will be considered strange, not the French one.
Now, an interesting question lying above that is: what can be revealed about the spirit of a language by analysing these small differences in directionality?
