Why did many Jewish religious leaders oppose Jesus?
They took offense at the way he interpreted the law of Moses.
Jesus gave new interpretations of Mosaic Law that the Scribes and Pharisees would not accept. For example, he healed on the Sabbath.
Jesus interpreted the Mosaic Law with a divine authority, that was greater than the authority of the Scribes and Pharisees.
Jesus criticized the legalism with which Scribes and Pharisees had been interpreting the Law of Moses.
: a strict adherence to the letter of the law, without due regard for the spirit and intent of the law.
Scribes and Pharisees especially were concerned about keeping the oral law that had been built up around the law of Moses. However, many of them made the oral law more important than the law itself (for example, regarding oaths and respect for parents).
Jesus predicted the destruction of the temple. The Scribes, Pharisees, and Sadducees distorted his words and said that he was speaking against the temple.
Jesus proclaimed his oneness with God the Father. Lacking faith, they felt he was speaking disrespectfully of God.
The Sadducees especially feared that Jesusí popularity might provoke reprisals from the Romans. For this reason, Caiaphas the high priest was the first member of the Sanhedrin to say that Jesus should be put to death.
Note: Not all of religious leaders in Jesusí day opposed him. Some deeply respected him (e.g. Nicodemus).