Jesus left the area because He knew the Pharisees were plotting against Him. This would not be the last time that our Lord withdrew from a region for self-preservation. Jesus always had His primary purpose of seeking and saving the lost (Luke 19:10) as His focus. Sometimes He faced His enemies, and sometimes He withdrew from them. His actions in specific circumstances were based upon His assessment of how He could best accomplish His work. Fear of men had nothing to do with His decisions. Even today, it is sometimes better to quietly withdraw from a hostile group and do one's work elsewhere.
Our Lord healed all of those in need who were among the multitudes that followed Him. It is likely that most of these people were present because of the miraculous healings (and the excitement associated with such), not because they were drawn to Jesus by His teachings. It is important to understand that no one can be saved today without the gospel (Rom. 1:16), but many opportunities to teach God's word are unavailable until a person has been treated with love and compassion. When people know that you genuinely care about them, it can only improve your chances of influencing them for good and reaching them with the words of life.
According to Matthew 12:16, Jesus didn't want those He was healing to proclaim Him to others. There were at least three reasons why: (1) These individuals were not really prepared to proclaim Jesus in a proper way; they could proclaim Him as a miracle worker but not as the Son of God, and Jesus did not desire the reputation of being just a miracle worker, (2) If they proclaim Him, it would only continue to make things worse between Him and the Pharisees, and (3) Jesus, in fulfillment of prophecy (cf. 12:19), would perform His ministry without unnecessary commotion (i.e., He was fully capable of making Himself known as He had been doing).
In 12:18-21, Matthew quoted a prophecy from Isaiah 42:1-4 concerning the Messiah and some of His attributes. The Messiah would be God's Servant (Matt. 20:28; Phil. 2:7). He would be loved by God and well pleasing to Him (Matt. 3:17). He would have God's Spirit upon Him (Matt. 3:16). He would "declare justice to the Gentiles"; this would be accomplished by Christ through His apostles after the church began (cf. Eph. 2:17).
The Messiah would also be known for His humility. Jesus' meek withdrawal from the Pharisees fulfilled this prediction about not quarreling or crying out. Jesus continued to work quietly on His Father's business. It was never His intent to "cry out" and blow His own horn, so to speak. Jesus' ministry was never about self-promotion.
Isaiah also wrote about the Messiah's compassion. The healing of the multitudes who followed Jesus fulfilled this prediction about the "bruised reed" and "smoking flax." A damaged reed that is perhaps not strong enough to stand up and smoldering flax that is nearly extinguished are appropriate representations of the sick, lame, and blind who were brought to Jesus for healing. A damaged reed would be considered by most to be of little use, and smoking flax, caused by imperfection in the fiber, is annoying. However, Jesus doesn't look on these people as being useless or annoying, and thus, unworthy of His time. He would heal their bruises and fan their dying energies into a flame--physically and spiritually.
Finally, Isaiah declared that "in His name Gentiles will trust." Not only would the Messiah be kind, humble, and gentle to His own people, but He would also provide hope to non-Jewish people.
This brief consideration of some of Jesus' attributes should encourage us to reflect upon our own lives. God calls us to be His servants, humbly submitting to His will in all things--just like Jesus! May we endeavor to be compassionate and willing to help others both physically and spiritually to the best of our ability--just like Jesus!