The Myth of the spoiled child is the idea it is a major problem that kids lack self-discipline, will power, persistence and the ability to defer gratification. Several authors, such as Martin Seligman, Roy Baumeister, Paul Tough, and Angela Duckworth (who uses the word 'grit' a lot) have argued that parents and teachers should put much emphasis on teaching kids these things in order to succeed.
Kohn's first crticism is that focusing on grit (and self-discipline, etc) as a virtue in itself does not make much sense because not everything is worth doing, let alone persisting in. A criminal with grit is even worse than a regular criminal. So before stressing things like grit, we should first reflect on what is interesting and worthwhile doing at all. Furthermore, says Kohn, persistence can, in some cases, be counterproductive and unhealthy. If you are digging a hole for yourself, it might be wiser to stop digging. The question is: when is it worthwhile to persist and when is it wiser to stop?
Kohn also challenges the empirical evidence for the value of grit. He points out that the famous marshmallow experiments done by Walter Mischel in the late 60s and early 70s have been wrongly interpreted by many modern authors. Modern authors like Jonah Leher say the experiments showed that kids who were better at delaying gratification later performed better both socially and cognitively and argue that we should therefore teach kids delay of gratification. But the experiments were about something else entirely, namely about the setting instead of the individual kid's self-control. Mischel wanted to know how kids could delay gratification and he found that the kids best able to do so were not applying "self-denial and grim determination". Instead, they distracted themselves by doing something interesting, so that not picking up the marshmallow wasn't even about self-control much anymore. (Read more about Kohn's analysis of the misinterpretation of the experiments in his book).
He also criticizes Angela Duckworth's writing and research. While he admits that self-discipline is associated with higher grades in school, he says that there is also a downside associated with self-discipline which is that those disciplined, high-grade receiving kids also tend to be more conformist and less creative. A core criticism of Kohn is that while it may be true that grit in a narrow task leads to better performance on that task, it also is associated with several sorts of downsides such as having less openness to experience and being less able to enjoy a complex mental life.
My take on this is that Kohn is right to point at the importance of the question of whether something is and remains worth doing. I agree that becoming good at something requires longer-term dedication but the important question is: when and why should you make such an investment? I have argued that the best basis for doing so is that you find the activity worth doing which means that you find it interesting, both in the sense that you enjoy doing it and find it important. When this is the basis for putting in effort, it won't require too much (if any) self-control (see Mischel's experiments). Rather, the activity fuels the process of proceeding. Read more about this here: Interests as drivers of competence development.