Someone can correct me if I'm wrong, but I'm pretty sure に is often used with verbs that involve interacting with a person. Particles can have more than one use, and に has multiple. The movement use is just one of them.
に is a very diverse particle with lots of uses, and most of them come down to being either the origin or destination of movement. I'll try to give some very generalized explanations of its use.
1. With いる or ある (and other derived verbs describing existence), it's used to mark where something is. It is entirely interchangeable with へ here, and its usage in this way is pretty straightforward.
2. With passive verbs and ~てある constructions, it's used to mark who did the thing being done. その小論文が私に書かれた。 This usage is also pretty straightforward.
3. With verbs of giving and receiving (上げる,もらう, etc.), it indicates the other party in the transaction: ie, in もらう, it indicates who gave whatever it is being given; the receiver would be the subject. This also works when verbs of giving and receiving are being used as auxiliary verbs.
4. With な adjectives, に is used to make an adverb.
5. With なる, に is used to describe the new state of things. It is often combined with こと and よう, with ようになる implying a lack of control or deliberation. Note that there are many other uses for ように and a complete explanation of all of those would be quite long.
6. With する, 決める, and other verbs relating to decision, に indicates the decision arrived at.
7. With most other transitive verbs not listed, に is usually used to describe where something is moving to. This can be literal or abstract and is sometimes not intuitive.
8. With intransitive verbs involving movement (ie 引っ越す
it indicates the location that one will be verbing to.
9. It's also used with a wide variety of words to indicate the time that something has happened or will happen.
There are a lot of ways to use に and it's a very difficult particle to translate a lot of the time. It also appears in a lot of compound particles with uses that have a tendency to confound beginners (にも especially, I think). The specific nuances of に have significantly hampered my comprehension of a passage many a time.