We neither have, nor need (in my opinion) an explanation. Electrons, like all fundamental particles, have a property known as “spin”. In other words they have an angular momentum. This property is intrinsic. However fundamental particles do not have dimension, they are not little spinning balls. The spin angular momentum associated with fundamental particles has some properties that are very strange, and completely unlike the behaviour of spinning basketballs, or gyroscopes, or figure skaters, or whatever. They have spin because they do. That's what "intrinsic" means. To ask "why" is either a silly question, or else a theological one.