The classification serves a democratic purpose.
Making laws, implementing them through the state and deciding legal disputes should not simply be concentrated in one unchecked authority. Separation of powers distributes functions and provides mutual checks. The judicial task belongs to the judiciary.
The branches are not completely disconnected. They interact within the constitution. What matters is that a judicial decision does not merely carry out a government instruction: judges are independent and subject to the law.

The other three answers
The four options do not name four equivalent branches of state power.
executive.
The executive chiefly comprises government and administration. It is part of the separation of powers, but not the branch to which judicial decision-making belongs.
press.
The press informs the public and can scrutinise power. It is therefore sometimes metaphorically called a “fourth power”. That does not make it one of the three state branches or turn judges into journalists.
legislative.
The legislature is the lawmaking branch. A parliament passes laws; a judge decides legal cases. These functions must be distinguished for this classification.
Independence does not mean complete isolation without checks.
Separation of powers does not mean state institutions never interact. The constitution determines their relationships and responsibilities. That regulated distribution helps limit power.
Public criticism of judgments does not change the classification. Judges remain part of the judiciary; the media report and comment freely outside the three state branches.
Article 20 paragraph 2 · Basic Law ↗Three state branches: judicial decisions belong to the judiciary.
Think of three functions as well as three names. The press option is a reminder to distinguish state power from public scrutiny.
Three words for this question
- die Gewaltenteilungseparation of powers
- Distribution of state functions with mutual checks.
- die Machtkonzentrationconcentration of power
- The accumulation of many decision-making powers in one institution.
- die Pressefreiheitpress freedom
- The protected freedom of journalistic reporting.
