‘And Jesus went out from there, and withdrew into the parts of Tyre and Sidon.'
Aware of opposition growing all around Jesus now withdrew again and moved into the areas around Tyre and Sidon. These were in non-Jewish territory to the north of Palestine, and outside the jurisdiction of Herod and the influence of the Jerusalem Scribes. Tyre and Sidon were two seaports on the Mediterranean coast in Phoenicia. Jesus had earlier spoken of them as cities which would have believed had they seen the Messianic works performed that were performed in Chorazin and Bethsaida (Matthew 11:21-22). This may in fact be partly why Matthew mentions their names, for now one of their residents will be given that opportunity, but the main reason is in order to signal the new turn that Jesus' ministry is taking. From now on He will spend much less time in Galilee.
It will have been noticed that (except in the mouth of Jesus - Matthew 11:21-24; Matthew 12:41) Matthew names no towns apart from Capernaum. He seems rather to favour districts, and even then it is seemingly in order to indicate movement between Jewish and Gentile territory. That is the case with this reference to the parts of Tyre and Sidon. Other similar references are as follows:
‘Coming to the other side into the country of the Gadarenes' (Matthew 8:28). Here He was coming to Gentile territory, and from there they ‘crossed over and came to His own city' (Matthew 9:1), which explains how He returned to Galilee.
‘Crossing over they came to the land, to Gennesaret' in Galilee (Matthew 14:34). This indicates that they had come from Gentile territory, which they had reached earlier by boat (Matthew 14:13), and which was on ‘the other side' (Matthew 14:22).
‘Entering into the boat they came into the borders of Magadan' (Matthew 15:39). This again indicates that they had come from Gentile territory, territory which had been reached after leaving Tyre and Sidon, by going via ‘the Sea of Galilee' (Matthew 15:29) and the regions of Decapolis (Mark 7:31).
‘The disciples came to the other side -- Jesus came into the parts of Caesarea Philippi' (Matthew 16:5; Matthew 16:13). This again indicates a venture into Gentile territory, after which they returned to Galilee (Matthew 17:22).
This suggests that the reason for mentioning the names is so as to indicate when He is in Gentile territory. This being the case it points to four visits to Gentile territory, Matthew 8:28 to Matthew 9:1; Matthew 14:13-34; Matthew 15:21-39; Matthew 16:13 to Matthew 17:22. Thus this one that now follows is the third, and longest such visit. It will be noted that in Matthew (but not in Mark) ‘the other side' is always in Gentile territory.