Dedicated to the Lord Jesus Christ Who loved us, gave Himself for us, and washed us from our sins in His own Blood; and to the Church, which is His body.

Matthew 4:12; Mark 1:14; John 4:1-3
On the surface, it might look like Jesus was running from a fight. Now that John the Baptist was out of the way (he had been imprisoned), it was inevitable that the Pharisees would attack Jesus.
One thing we can be sure of is that there was no fear on our Lord's part. On other occasions He demonstrated that no one could do anything to Him if He didn't allow it (Luke 4:29-30; John 7:30, 44-46; 8:20, 59; 10:39).
We can assume that Jesus left because He knew it was God's will. On another occasion when His half brothers dared Him to go to Jerusalem and confront the Pharisees, He told them that it wasn't time for Him to go yet (John 7:1-6). A lesser man would have been intimidated into showing His superiority.
Jesus was the most selfless person who ever walked the earth. He did not come to earth for Himself, but for us. If He would have defended Himself, we would have never been saved. The humility of Jesus was surely interpreted by some to be weakness, but in truth it was love. Not love for Himself, but love for a dying world of which He was the only hope.