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Why?
The word "school" is used as a countable and an uncountable noun.
It's an uncountable noun used without an article when you are talking about somebody attending a school. It's a countable noun if you are talking about somebody doing something other than learning or studying there.
She's still in school = She is still studying there.
If you say "She's still in the school", it doesn't mean she studies there; instead, she is there for any other purpose e.g. just visiting or paying your tuition fee.
She's going to school. It means she's a student there.
She's going to a school. Maybe to find a job or to see how a school looks like.
As you have noted, the countable noun gets an article. She wants a single divorce. Divorce as an idea is not countable.
"School" in the first two examples refers to the process of receiving education at institutions of learning. Again, it's an abstract process, not a concrete, countable thing. "In school" and "going to school" mean "engaged in formal education."
"A school" means a specific institution, not the process. So, you can say "She is going to a school" or "She is going to the school," when you are referring to a concrete school and not the process.
