What is objectively and subjectively

Objective refers to a viewpoint or opinion that is not influenced by personal feelings, interpretations, or bias. It is based on facts and evidence.

Subjective, on the other hand, refers to a viewpoint or opinion that is influenced by personal feelings, interpretations, or bias. It is based on one's personal experiences, beliefs, and emotions.

What is it called if someone prefers something over another and calls it objectivity, but really it is subjectivity

This is called subjective bias or subjective preference masquerading as objectivity. It occurs when someone presents their personal opinion or preference as an objective fact, even though it is influenced by their personal feelings and biases. This can lead to a false sense of objectivity and may impact decision-making processes.