When you look into what James Cameron was doing with that scene, and what followed. It goes further to show how badly the makers of the reboot messed up.
In the director's cut of T2, the first awkward smile was just that, a first awkward attempt. John Conner says something along the lines of keep practicing. Which ties into one of the main plot-lines that was cut from the theatrical release, that they change the chip in the Terminator's head to learning mode. And so then further into T2 Arnold does smile a few more times, the Terminator is actually mimicking young John in the way he would smile. Curling the side of the mouth up, in a half smile, cheeky way. James Cameron does have all his shit sorted out.
And later again, more natural
(and also the chip mode switching scene)
Terminator having spent decades fitting in around humans.
Yeah!