With Newton's third law, why are things capable of moving?

Question

I've got a rather humiliating question considering newton's third law "If an object A exterts a force on object B, then object B exerts an equal but opposite force on object A" -> $F_1=-F_2$ Considering that, why is there motion at all? Should not all forces even themselves out, so nothing moves at all? When I push a table using my finger, the table applies the same force onto my finger like my finger does on the table just with an opposing direction, nothing happens except that I feel the opposing force. But why can I push a box on a table by applying force ($F=ma$) on one side, obviously outbalancing the force the box has on my finger and at the same time outbalancing the friction the box has on the table? I obviously have the greater mass and acceleration as for example the matchbox on the table and thusly I can move it, but shouldn't the third law prevent that from even happening? Shouldn't the matchbox just accommodate to said force and applying same force to me in opposing direction? I've found a lot of answers considering that question but none was satisfying to an extend that I had an epiphany solving my fundamental problem I've got understanding it.

Answer 1

If you apply 2 equal and opposite forces to an object, the "net force" is zero, and nothing happens. This is not what happens in response to Newton's 3rd law.

When you apply a force (to anything), you will sense the opposing force dictated by the 3rd law. If you didn't, the object would be instantly** displaced. The "reaction force" that you feel is due to the inertia of the object---i.e. the fact that it cannot start moving without a force. Imagine pushing on something that is 100X more massive than you are. You will feel the reaction force for a very long time, because the object accelerates VERY slowly. By contrast, if you push on a spec of dust or a ping-pong ball, you might feel nothing. With a very light object, the same reaction force is there, but only for the very short time it takes to accelerate.

**"Instantly" means that something travels between 2 points in zero time. This requires infinitely high acceleration, and therefor infinite force. for a very light object, the reaction force is there---it just does not last long enough for you to feel it.

Answer 2

When looking at a pair of forces that are related via Newton's third law, those forces act _on_ different objects. Because the forces exerted by A on B and by B on A act on different objects, they could never balance each other.

When you're trying to determine whether object A accelerates, the key question is whether the forces everted _on A_ are balanced or not; all of those forces are exerted on A by objects other than A. The forces exerted _by_ A are irrelevant to determining whether or not A accelerates.