They worshiped her because it provided protection and wisdom.
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It's not a matter of liking or disliking, they felt obligated to worship her due to their religion. Athena (Minerva) was a very important goddess for both the Greeks and Romans. In fact, she was one of the Capitoline Triad for the Romans.
The Parthenon in Athens was where people would go to worship Athena in Greece.
Athena did not worship, being a Greek goddess, however Athens was named for her believed to be her favored city.
The Roman form of Athena is Minerva.
Believe it or not, the Temple of Athena was made as a place of worship and tribute to the Greek Goddess Athena.