"How come you want to learn English?" <--This is very common in everyday conversation in the US.

"How come" is the same as "Why".

Another way to ask the same question is:

Why do you want to learn English?

"how come" is asking for an explanation. (short for: How did this come about, that.. ?) It can be more emotional.

"why" is asking for a reason, or a purpose. It's more detached.

Example:

Mom: "You can't go outside today."

Child 1: "Why not?" <-- asking for a reason. (Just curious, maybe not really bothered by Mom's decision.)

Child 2: "How come?" <- needs an explanation. (Maybe the child disagrees with Mom and needs to be convinced.)