$(a)$ Let's say A person is pushing an object. Then the object will put a force on the person equal to the force the person is putting on the object (because of Newton's third law). Then the person should move backward because of the opposing force. But clearly, the person moves in the same direction as the object while the person pushes it. Is there something wrong with my reasoning?
$(b)$ Let's say I am pushing against a wall with force $F$, then the wall will push me with force $F$ (because of newtons 3rd law). Because The wall is pushing me with force F, then I will (because of newtons 3rd law), push the wall with force $F$, this will add up with my previous force to $2F$. If I keep doing this indefinitely, then I can say that I am pushing this wall with a force of $\infty$ $N$ and the wall is pushing me with a force of $\infty$ $N$. That would mean I will get crushed and the wall will get destroyed. But clearly, that does not happen. Again, where am I using Newton's 3rd law in the wrong way?