So Time thinks that not letting an already arrogant kid skip two grades is "failing" her.
The most important thing for a school age kid is to become well-socialized.
The correlation between skipping grades and turning out well is just a correlation - it may be that those who were not allowed to skip were so messed up socially already that they were less likely to convince their schools to let them skip grades. In contrast, if you're well-adjusted and smart, it's more likely that you'd be able to convince school administrators to allow you to skip a grade. And, of course, Time misses that distinction, making it into a clear case of "the more grades skipped the better."
I actually have experience on both sides of this issue. My principal would not allow me to skip 3rd grade, despite my teacher's and parents' requests. On the other hand, in junior high, I was allowed to test out of three years of math.
I can assure you that any negative effects of skipping grades are far outweighed by the effects of holding students back. The latter fosters resentment and frustration, which doesn't help social aspects much. For the former, as long as you're sharing classes with advanced students in higher grades (and why wouldn't you be?), the older students are very welcoming.
Also, arrogance isn't a negative quality in talented math/science students -- it's essential. You just can't get really good at math unless you believe you can figure out difficult problems yourself. Maybe you don't have to admit it, but there's a point where denying your abilities looks foolish. The "I've played a lot of Number Munchers" line only works for so long.
"So Time thinks that not letting an already arrogant kid skip two grades is "failing" her."
Kids tend to become less arrogant when placed among intellectual peers, even when those peers are several years older. It's because people naturally compare themselves to the folks around them. If they're always smarter than their peers, they'll assume they're smarter than everybody. If instead they're always younger than their peers - well, they'll grow out of that. ;-)
Going to Amherst and majoring in physics was perhaps the most humbling experience in my life, because it was the first time I wasn't the smartest one in the room. I suspect this is the real point of the university system - by bringing all the smart kids together, recursively, you teach them that there's always somebody smarter than them.
I think modern society's damning of "arrogance" and pride is also a bad thing. The fact that we aren't all as self-confident as some of the brightest doesn't give us the right to try to strip them of their own self-confidence.
The most important thing for a school age kid is to become well-socialized.
The correlation between skipping grades and turning out well is just a correlation - it may be that those who were not allowed to skip were so messed up socially already that they were less likely to convince their schools to let them skip grades. In contrast, if you're well-adjusted and smart, it's more likely that you'd be able to convince school administrators to allow you to skip a grade. And, of course, Time misses that distinction, making it into a clear case of "the more grades skipped the better."