I'm a 40 year old mother of 3 arguing with her husband.
Homework ? Say what ?
Does the friction between the tires and the pavement of a turning car "cause" the Centripetal Acceleration that is pushing the car towards the center of the turn arc ?
Sorry, but I don't answer homework questions.
Over the years, people have (more than once) tried to get an answer to an academic question by claiming they were "just curious" about an aspect of physics. Instead of either answering every such question, or refusing to answer any such question, I simply use my judgement on the likelihood that someone would, outside of academic work, ask a question in a way that they have phrased a question. I admit I lack the perfect ability to determine this. So, what I instead do is simply delay an answer for enough time that (1) if it was an academic question, my answer would be of no help and (2) if it was NOT such a question, the delay would not matter. I hope my answer will be soon enough to resolve the differences between you and your husband.
ANYWAY, let me give a complete answer, including a little background.
Any object in motion will continue in its straight line motion UNLESS that object is acted upon by an external force. This includes a car going down the pavement of a road. If the road happens to curve, then the car will continue in its straight line -- and go off the road -- unless an external force acts on it.
When a car does go around a curve, there MUST be a force causing it to not go straight. Physicists call such a force -- whatever its nature -- the "centripetal" (ie, "center seeking") force, because it is acting on the car to make it move towards the center instead of going in a straight line.
Whoever said, that the friction between the tires and the pavement is the centripetal force, is correct. Imagine, if you will, what would happen to a car, approaching a curve, when there is no such friction -- a curved road covered in ice, for example. The car will continue in its straight line and go off the curve in the road.
To answer the (possible) next question, the "centrifugal" force is actually a pseudo-force felt by anyone inside the car as it accelerates (ie, changes the direction of its velocity). Any such person will experience a "force" that seems to pull them in the direction opposite to the centripetal force. The centrifugal force is NOT pulling the car to the outside of the curved road, that effect is simply the momentum of the car that causes it to continue in a straight line, and off the curved road.
I normally offer to answer further questions, but (unfortunately) I will be out of town next week.