Question: I've been doing physics problems regarding cars for a while. I understand that there is a static friction (which appears when the wheel is rolling) and kinetic friction (which appears when the wheel is sliding). However, the way I'm visualizing it, static friction between the tire and road should not stop a car. In fact, when I asked this question to my teacher a long time ago, he said that it is actually the friction between the axle and the wheel that stops the car, and the road friction actually helps the car to move. But I know that when the car slips, the friction decreases and thus stopping time increases. How could this possible be linked to the axle? What is going on?

Answer: 
Imagine a car just going along at constant speed. Do your free-body diagram. The net force on the car has to be zero. So the wheels have to be exerting on the ground (net at least) only a vertical force. 

Now imagine the car decreasing speed. There has to be a force opposite to the velocity. Free-body time again. The force on the ground has to include a force component that opposes the motion of the car. The wheels are the part touching the ground, so they must be supplying that force.

Remember your Newton's laws. To stop the car must be acted on by an external force. If you call the wheels "part of" the car, then the stopping force has to be applied by the ground. Meaning the wheels have to push back exactly as hard.

If you call the wheels "not part of" the car, then you can describe it as the braking mechanism applying a force to the wheels. Then it's "the wheel's problem" what it does with that force. But in that case, the car is stopped by friction between the brake mechanism and the wheel. It may be that your teacher is trying to get you to think that way.
cars stop with their brakes, which produce friction at the inside of the wheel assemblies as the wheels rotate. This friction force retards the rotation of the wheels and dissipates the kinetic energy of the car into heat in the brake parts. 

since the wheels are in rolling contact with the pavement, and since the wheels are being slowed by the brakes, the pavement is pushing back against the wheels at their contact point with the pavement in a direction that opposes the movement of the car. So the car as a whole slows down.