No, He didn’t heal everyone He met; those who disbelieved and turned their backs on Him had no part in the blessings He offered. This, incidentally, should be a warning to us of the dangers of disbelief.
But Jesus did heal large numbers of people who came to Him, and He performed other miracles, as well. One reason was because of His compassion for those who were hurting and had no hope. The Bible says that when a large crowd gathered on one occasion to hear Jesus, “he had compassion on them and healed their sick” (Matthew 14:14). And He still has compassion on us in our suffering, for He loves us.
The main reason for Jesus’ miracles, however, was to demonstrate that God was with Him, and that He was the promised Savior sent from God. You’re right — not everyone was persuaded; some of His enemies even claimed He did them through the devil’s power. But others did believe — and so should we.
The greatest miracle of all, however, was Jesus’ resurrection from the dead. It was the ultimate proof of His divinity, and demonstrated for all time that He has conquered sin and death and Hell and the devil. Don’t be like those in Jesus’ time who turned away and wanted nothing more to do with Him, but by faith open your heart to Christ and welcome Him into your life. Then even greater miracles will take place — the miracle of forgiveness, and the miracle of becoming part of God’s family forever.