In one sense it is justified by the overall success if Newtonian Mechanics; still, one can ask are there arguments that can justify it from other principles; ie principle that are * a priori* in nature. For example, Kant supplied one, in his Metaphysics of Natural Science; and to which he added the remark:
“[Newton] by no means dared to prove this law a priori, and therefore appealed rather to experience”
His argument is as follows:
(i) if all changes of matter are changes of motion;
(ii) if all changes of motion are reciprocal and equal (since one body cannot move closer to/farther away from another body without the second body moving closer to/farther away from the first body and by exactly the same amount); and
(iii) if every change of matter has an external cause (a proposition that was established as the Second Law of Mechanics), then the cause of the change of motion of the one body entails an equal and opposite cause of a change of motion of the other body or, in short, action must be equal to reaction
Is the following argument more basic? In that (ii) is deduced from considerations of symmetry:
Consider an action: what does this mean? A substance can't act on itself, for how can we say it acts now as opposed to then? To make this concrete, consider a classical electron - its negative charge doesn't act on itself - otherwise it wouldn't have any cohesion.
It acts then, on an other; and then on contact; but by symmetry, ie swapping the one substance with the other, the same situation is obtained.
Hence every action has an equal an opposite reaction
Where equal and opposite are not to be understood in quantifiable terms; but in the terms outlined above.
And this argued as an outcome of action by contact; and by contact that one is simultaneous in place and time with another; and that this relation is symmetric.