In Matthew 8:8 and Matthew 15:27 about the centurion and the Syro-Phoenician woman, both are gentiles, but Jesus healed the centurion's slave without question, and to the Syro-Phoenician woman he said "it is not fair to take the children's bread and throw it to the dogs". Could you explain this?
As to Matt.8:8, first, Luke 7:3 tells us that Jesus was asked by the Jewish elders of the town to do this (so that He was fulfilling a Jewish request). Secondly, we know from Luke 7:5 that this man was a Jewish proselyte (as when Jesus heals a number of Samaritans, while not technically Jews (cf. Matt.10:5 where they are listed by the Lord separately from Jews and gentiles), they fall into the category of those within Israel in like manner to the gentiles who were associated with those who came into the land). Thirdly, as a member of the government of Judea, there is also the principle of supporting the authorities, no matter what you think of them. The Syro-Phoenician women didn't have any of these factors (any one of which may well have been enough to override the ruling principle here that Jesus had been sent "to the lost sheep of Israel", not to the gentiles). It's also important to remember that, after expressing her faith in a marvelous way, He did indeed heal her daughter.
Salvation came through the Jews by the Messiah, Jesus Christ (Jn.4:22), and had to be proclaimed first to the Jews as the unique people of God (Rom.1:16; 2:9; 2:10). But God in His great mercy sent His Son to die for the sins of the entire world so that all the world might be saved, gentiles and Jews alike (Rom.3:21-31).
Please see also the following links:
Procedures and Reception of Jesus' Ministry (including the gentile issue)
The Course of Jesus' Ministry
Jesus' Cursing of the Fig Tree
Is Jesus the only One who ever Cured Blindness?
Healing by Touch
In Him who has deigned to make us part of His Body even when we were His enemies, our Lord and Savior Jesus Christ.