Why did Jesus obey Jewish Law?
The answer is simple:
Jesus obeyed Jewish Law because Jesus was Jewish.
The answer is not more complicated than that.
Because Jesus was Jewish, He obeyed the Mosaic Law, worshipped God in the Jewish Temple, attended a Jewish Synagogue, taught from the Jewish Scriptures, and even obeyed many of the Jewish oral traditions. There is much evidence that He even followed many of the teachings and traditions of the Pharisees.
Should We Obey the Jewish Law?
However, when people talk about Jesus and the Jewish Law, what they might really be asking is whether or not we, as followers of Jesus, should also be obeying the Jewish Law.