I think the author is trying to contrast the middle and high school teachers to play the latter's approach up compared to the former's, but I think both have been effective in their own way. The middle school teacher couldn't have recommended Eunyung for work, and at his age what mattered most was showing him that she cared. At that age, telling a child they're not so different from everyone else and that there's a path ahead even from misery are important motivational boosts. Heck, just showing to him that there are good adults in the world is a step forward.
But in high school, motivational stories don't work anymore, you have to put in some real work to not only show the path ahead, but to prod them to take the first steps. And it takes a real teacher (though it seems to me that Korean homeroom teachers have to be more like social service officers) to diagnose what the problem is in a case-by-case basis and use a targeted approach to obtain the desired outcome. I don't think the job training opportunity was favoritism at all: the teacher identified a promising student on whom that specific intervention had the highest chance of working and went for it. Other problem kids need other solutions.
First and foremost, the teacher was able to see that Eunyung has a good temperament and is able to put in the work if motivated, and that the main issue is that, beneath the superficial semblance of nonchalance and self-confidence, Eunyung doesn't see himself as being able to amount to much. Given that only his closest friends are aware of that, this teacher is nothing short of amazing. Respect where respect is due.