the children's bread = the bread of the children, with emphasis on children. Figure of speech Enallage.App-6.
children's. See App-108.
dogs = puppies, or little household dogs; this is true only of such. Dogs are not cared for (in the East) when grown. The Lord used the Figure of speech Hypocatastasis (App-6), implying that she was only a Gentile, and thus had still no claim even on that ground. Gentiles were known as "dogs" by the Jews, and despised as such (Mat_7:6; 1Sa_17:43. 2Sa_3:8; 2Sa_9:8. 2Ki_8:13. Php_1:3, Php_1:2).