In the figure below it is stated that the friction force should always be greater than the tangential force in order to prevent slipping between two frictional wheels. My question is that if we apply Newton's second law to that contact point won't the tangential force resultant point upwards with the direction of the friction since the tangential force is larger and thus the wheels have an opposite rotating direction?
The concept behind
the friction force should always be greater than the tangential force
is that the maximum friction force should be greater to the force that causes the rotation of the wheel. If you try to apply more torque, then there will be slipping.
This is very similar to the following concept:
If a small force $F_A$ is applied, then the friction force will only be equal to that force $F_A$ and the box will not move. If $F_A$ exceeds the maximum friction force then the box will slide.
Important Sidenote: That sliding motion is what we usually consider as motion, and sometimes get confused in the case of the gear the OP presented. I.e. the rotation again is considered motion. However, in the case of the gears there is no sliding -- i.e. for the contact point of gear A and gear B the relative velocity is zero, or in another way the move in unison.