If you are digging for some underlying principle by which Newton's Third Law could be deduced from the physics and mathematics known to Newton, I would answer "there is none". It was a testable hypothesis consistent with the available physical evidence. Assuming its truth allowed for additional testable conclusions to be reached. That is pretty much all that one can ask of a physical principle.Yeah, I know that the contact force is actually Electromagnetic force between the constituent molecules.
But I think at the time of Newton this fact was quite unknown. So, is there any explanation why Newton’s Third Law occurs/exists purely on the basis of macroscopic level?
It is in the nature of things that first principles cannot be deduced from nothing. They have to be guessed at based on experimental results. That's how science works.