Why did the disciples think they had nothing to do with the Canaanite woman?
The disciples thought they had nothing to do with the Canaanite woman because they recognized she was a Gentile. The covenants were Jew only, with no Gentiles included, so they considered her outside Israel's covenant promises and wanted Jesus to send her away as a nuisance.
Les explains that the disciples had already been in Christ's presence for some time, so they too understood she was a Gentile and that they had nothing to do with her. They urged Jesus to send her away because she was a pest and nuisance, crying after them. The underlying reason was covenant: Jesus said He was not sent but to the lost sheep of the house of Israel. There were no Gentiles in those covenants; it was Jew only. So the Gentile woman was almost presuming upon something she had no right to presume, especially by addressing Him as 'thou son of David.'
But he answered her not a word. And his disciples came and besought him, saying, Send her away; for she crieth after us.
More Questions
What did the disciples mean when they asked Jesus to send the Canaanite woman away?
The disciples' request to 'Send her away' meant 'Lord, get rid of her,' because they regarded the woman as a pest and a nuisance who had been tagging along after them.
Why were the disciples so annoyed by the Canaanite woman?
The disciples' irritation makes sense because the woman's crying after them had likely gone on for several days everywhere they went, and they reasoned that she was a Gentile they had nothing to do with.