Skipping school is most often something done without permission, and that sense contributes to its rudeness. The Oxford English Dictionary gets at that sense in its phrasing of this definition ("skip, v.1," def. 6b):
6.b. To absent oneself from, stay away from.
"To absent oneself" suggests that the student is usually the one deciding their own absence. Indeed, skipping school, or a phenomenon like "senior skip day" (Wikipedia), is very frequently illicit. Besides the inherent challenge to authority posed by absenting oneself, educators and law enforcement may associate skipping with other negative behaviors:
These teens may also drop old friends and activities, skip school, lose interest in school, receive low grades, sleep in class, lose concentration, and have trouble with memory. (Justice.gov)
If the threat of fines or jail time isn't enough to prompt parents to address truancy, research suggests that teens who regularly skip school are more likely than their peers to drop out of school or experiment with drugs and alcohol. (US News)
Often, the usage occurs when the parents do not know that their child is skipping. That said, sometimes parents may permit skipping school as well, if they see a specific need that goes outside of socially sanctioned cases for absence like a funeral or a religious holiday. One parent explains allowing a "mental health day" in terms of skipping:
In fact, I’ve let my kids, including my preschooler, skip school several times since then, and will continue letting them do this as they get older. Admittedly, my work-from-home job affords me the flexibility to keep them home on a whim. But more importantly, I’ve come to realize something: Kids need mental health days, too. (Today's Parent)
That usage is as close to neutral as it gets, but there's still a slight sense of irregularity. Skipping is unannounced and unapproved by the school. Asking a teacher to skip would be regarded by many as impertinent.