“What causes a child to have speech problems?”

There are many causes, and it may not be just one cause. Do you have a pediatrician that you check in with regularly? If so, I would start by letting the pediatrician know. They may refer for a hearing and speech/language evaluation, among other things, to determine cause(s).
Hope that helps! Best wishes. 

"Speech problems" is not specific. There are many etiologies that could cause or contribute to difficulties with speech. You need to ask the doctor for a prescription order for speech therapy evaluation or a referral for a speech pathology consult and you need to get an assessment from a speech language pathologist and work with that professional on your kid's needs. Early intervention is key, so don't stop asking until you get a doctor to write you a referral order for speech therapy evaluation.