Barnabas is mentioned for two reasons. First, he was well known to Galatians, having joined Peter on the first missionary journey (Acts 13:1 – 14:28). Second, he was an influential leader in Antioch and someone who clearly had a heart for Gentile mission. The fact that he was convinced by Peter’s actions to forsake eating with the Gentiles demonstrates how powerful Peter’s influence was.
13 And the rest of the Jews acted hypocritically along with him, so that even Barnabas was led astray by their hypocrisy.