Supervision is not the same as operating a school.
State supervision means that schooling does not operate outside public responsibility. It also matters when a school is not operated by a public body.
The Basic Law expressly permits private schools and sets conditions for private schools replacing public provision. Private operation and state supervision can therefore coexist.

The other three answers
The other answers give false premises or fail to identify the legal basis.
because there are only public schools in Germany
Private schools also exist. Article 7 protects their establishment, so “only public schools” is false.
because all students must have a school diploma
Compulsory attendance and actually obtaining a qualification are different things. A universal guarantee of graduation is not the basis of supervision.
because there are different schools in the federal states
Different school types and state rules do not explain the constitutional duty. Article 7 is decisive.
“The state” here does not mean only the federal government.
School supervision is organised within state responsibilities. The constitutional wording does not automatically put a federal ministry in charge of every school.
Supervision concerns responsibility and legal requirements. It promises neither identical schools across all states nor a particular qualification for every person.
Article 7(1) · Basic Law ↗Why school supervision? Article 7 of the Basic Law.
When the question asks “why”, look for the legal basis.
Three words for this question
- die Aufsichtsupervision
- Public oversight of compliance with relevant rules.
- der Schulträgerschool operator
- The body or organisation operating a school.
- die Privatschuleprivate school
- A school operated by a non-state body.
