Why was Esau hairy?

"Now the first came forth red, all over like a hairy garment; and they named him Esau." (Genesis 25:25)

That's just the way the myth was constructed. My guess is that it was an attempt by the ancient Israelites to explain why the name "Edom", a region neighboring ancient Israel, means "red" in Hebrew. The Bible traces their ancestry to Esau, so it made sense in a mythical context to give the Edomite ancestor a body covered with red hair.

Plus giving the ancestor of one of their main rivals a hairy body implied that he was wild and animal-like. Assigning negative qualities to an enemy and his ancestors is a dirty trick that goes back many millennia.

Genetics

Because his mum ate lots of goat, which was a popular meat back then. That where the saying "you are what you eat" came from. You eat lots of goat, you have hairy babies. You eat lots of candy, you have sugar babies.

Because he didn't use to shave!