Q:

Equal, opposite forces in Newton's third law

For every action, there is an equal and opposite reaction.

Look at this free body diagram from an exercise where a man pushes a box up an inclined platform:

I don't see all those "equal and opposite" reactions here. If the man pushes on the box, the box pushes on the man as well, and if the platform pushes on the box, the box also pushes on the platform, so why aren't those forces drawn here? The box also pushes on the air (P) and the air on the box but if those forces were equal wouldn't the box not move? I mean, if A pushes on B with force F and B pushes back on A with force -F, how come anything moves? Is it because the have different masses? Would that make this "opposite and equal reaction" not equal then? I'm confused.

A:

The key point is that

Newton's 2nd law applies on one object (or system).
Newton's 3rd law applies "between" two objects (or systems).

The action/reaction force pair do not cancel out because they don't act on the same object (or system).
You are right that the box exerts a force on the ramp $F_\text{box on ramp}$ and that the ramp reacts with an equal-but-opposite force on the box $F_\text{ramp on box}$:
$$F_\text{box on ramp}=-F_\text{ramp on box}$$
Both only one of them acts on the box. Only $F_\text{ramp on box}$ acts on the box. When you set up Newton's 2nd law, you only include forces that act on the box, because only those forces will have any influence on the acceleration of the box. All other forces - including forces that the box itself causes on something else - are irrelevant for the motion of the box.

