Why did Paul appeal to the Roman authorities after being rejected by the Jews?
Paul appealed to the Roman authorities because the Jews rejected him and his message, making their final decree to have nothing to do with him. Israel continued rejecting her Messiah, so Paul had to make his final move to the nation, and the Roman authorities came to his rescue.
Les explains that Paul went to Jerusalem contrary to many warnings, which raised discussion about whether he was being pig-headed, should have listened, or should have stayed away. Les sees that Paul got to Jerusalem in spite of roadblocks because this was where he had to make his final move to the nation of Israel. The Jews had to make their final decree away with him; they did not want anything to do with him or his message. Therefore he had to appeal to the Roman authorities, and they came to his rescue. Les notes that Israel continues to reject her Messiah, and because of that rejection and fall, as Romans chapter 11 shows, salvation goes to the Gentile. In Acts chapter 27, Paul had not succeeded in making any dents in the hard armor of the Jewish people.