Beorn

[the phantom]

Why does he have to fit?

Davem gave a great answer to this, but I'd like to say a bit more.

It is human nature to try and make sense of things. When you are presented with something new, you examine all the facts surrounding it and attempt to give it a place in your mind.

Don't you? (if not, then I'm worried about you)

When you try a new pie, you ask what is in it and how it was baked. And if the person tells you that they don't know, and that they merely placed the pan in the oven and the pie magically appeared, would you honestly be satisfied with that answer? Would you just stupidly say, "Oh, okay, I guess it's an enigma", or would you insist on a better explanation?

Tolkien was creating a world with mysteries and enigmas and unexplained phenomena (just like the real world)

Well, as D already detailed, Tolkien wasn't creating that kind of world. He liked to explain everything. And with good reason! Humans prefer things to be known. You are right that there exist mysteries and enigmas in this world, but surely you understand that existence does not equal acceptance. Mysteries and enigmas are not accepted in this world. When something unexplainable happens, teams of scientists are assigned to reveal the mystery, and experts everywhere come up with logic based theories to explain the mystery.

It is the same with Beorn. He doesn't make sense in Middle Earth with what we know about Middle Earth, and so he is a mystery. And so now we, the experts, need to come up with logic based theories to explain Beorn.

As I've said on other threads, just because a book can be found in the fantasy section does not mean any old silly thing can happen in it and that we must accept it.