Why is "Primary School" in quotes? Are you suggesting it isn't a primary school?
The name of the new school is "The Primary School". It looks like the title rewriter decided to try to put the name in the title, but left out the "The", resulting in the confusing title we now have.
A better rewrite, if the name must be incorporated, would have been "Inside Mark Zuckerber's new 'The Primary School': Private, but free" or "Inside Mark Zuckerber's 'The Primary School': Private, but free".
In many countries of the world, primary schools are schools that cater to classes between kindergarten and high/secondary school.
Calling a primary school "The Primary School" is like calling a brand of bottled water "The Bottled Water".
What's next, Facebook?
Oh.....