My teacher told me that this was because frictional force resists relative motion between the engine and the car. However, in this case it seems to allow relative motion between the ground and the car.
[...] it seems to allow relative motion between the ground and the car.
While there is relative motion between car and ground, there is not relative motion between wheel and ground. And that's what matters, because that's where the friction is.
Think of walking. Your body moves relative to the ground. But at each step, your foot on the ground is stationary. Your foot pushes on the ground backwards. Static friction holds back forwards to avoid that your foot slides.
On a car's wheel, the same happens, just at each new point that continuously comes in contact with the ground. For that short moment that it is in contact, that point is stationary and there is no sliding. That point pushes backwards, and so a static friction pushes forwards to avoid sliding (to avoid wheel spin).
Also, is friction a reaction force?
You can think of static friction as a reaction force, if you will. It only exists because your leg - or the car's wheel - applies a force backwards on the ground.
The torque applied to the wheel creates a rearward force on the ground which is opposed by the static friction force acting forward on the wheel by the ground.
A free body diagram of the car shows that the static friction force is the only external force acting forward on the car and is therefore responsible for accelerating the car forward. It allows relative motion between the car and the road due to rolling of the wheel, without relative motion between the surface of the tire and the surface of the road In the form of skidding of the wheel.
And yes, friction is a reaction force.
Hope this helps.
Think about swimming. You can propel yourself forward by pushing against the resistance of the water, but once you stop making the effort the resistance of the water brings you to a stop. So the resistance of the water plays two roles- one is that it gives you something to push against when you want to move, and the other is to bring you to a stop. Friction plays the same two roles in the case of the car. When you want to drive off, friction allows the tyres to grip instead of spin. When you stop accelerating, friction will act to slow you down.
In this case, friction prevents the car tires from slipping on the ground. That way the car's wheels can grip the ground properly and spin pushing the ground backwards and the car forward.
Otherwise the the wheels would slip making it difficult for the car to move as it happens on ice and rainy days.
in this case it seems to allow relative motion between the ground and the car
Assuming the car tires don't slide on the road, friction does no work in retarding the car. It doesn't even accelerate the car. It just improves the traction. It helps the tires to push on the ground.
Frictional force resists relative motion between the engine and the car
Remember, the small depressed area of tire in contact with the road doesn't move so friction doesn't do any work (assuming it doesn't slide over). Friction can oppose relative motion when it does work (like when something slides over something else).
Until and unless the point of contact doesn't slide on the road there is relative motion. When a car moves, the wheels start pure rolling on the road and the point of contact remains stationary w.r.t. the road.
So static friction is the only force acting on the wheel which acts in such a way that it opposes the impending motion of the wheel (which is backward) and accelerates it in the forward direction.