As a non US resident, I don't really get it.

Can someone explain why is it such a crime to run a school? (illegal maybe, but I guess the purpose is still to teach to young people). Shouldn't we promote the creation of schools?

Not a US resident either but there are zoning laws to ensure comfort for everyone. The article mentions the sorts of discomfort suddenly opening a school in a quiet neighborhood can cause. It causes upset especially when it's an elite private school that the neighborhood can't even benefit from at all.

> Neighbors complained about noise, security guards, and hordes of traffic

> For almost a decade, the Zuckerbergs’ neighbors have been complaining to the city about noisy construction work, the intrusive presence of private security, and the hordes of staffers and business associates causing traffic and taking up street parking

Doing so in a residential neighborhood is fraught with possible legal problems:

The city, the neighborhood association(s), the county and the state likely have questions about the school, whether it is legal, licensed, and inspected as specified by all jurisdictions. What about any traffic impediments it causes? Fire hazards, who certified the school, the teachers, the equipment, is food served, is it a commercial or nonprofit concern, on and on. You get my drift.

It's more that he moved into a dense residential neighborhood of single family homes and started buying up all the neighboring houses (11 so far, and he's offered on even more!) to create a massive walled off compound for himself, on which he then opened a private school for his family and his friend's kids. If he wanted to build some billionaire private compound why not go do that somewhere more remote where he could just have a ton of land enjoy doing whatever he wants with privacy and not bothering everyone instead of greedily hoovering up all family homes in a dense metro neighborhood. Not only is he decreasing housing in an area where it is desperately needed but he's bothering his neighbors with construction and noise with neverending renovations, increased traffic for all his staff, and his security team now harasses the neighbors when they're walking around on public sidewalks in front of their own houses.

Selection bias. Live and let live people don't wind up living in Palo Alto.