KJV - But Jesus said unto her, Let the children first be filled: for it is not meet to take the children's bread, and to cast it unto the dogs.
HCSV - He said to her, “Allow the children to be satisfied first, because it isn’t right to take the children’s bread and throw it to the dogs.”
NIV (1984) - “First let the children eat all they want,” he told her, “for it is not right to take the children’s bread and toss it to their dogs.”
ESV - And he said to her, “Let the children be fed first, for it is not right to take the children's bread and throw it to the dogs.”
and so on....
Of these versions, the NIV comes closest to the meaning. But these next three do the best job:
YLT - And Jesus said to her, `Suffer first the children to be filled, for it is not good to take the children's bread, and to cast [it] to the little dogs.'
Amp - And He said to her, First let the children be fed, for it is not becoming or proper or right to take the children’s bread and throw it to the [little house] dogs.
ISV - But he kept telling her, "First let the children be filled. It is not right to take the children's bread and throw it to the puppies."
When we read the first versions, we get in our mind an insult, that Jesus is referring to this woman's ethnic group as dogs. The mental image that arises is Jesus turning his back on her in a huff, throwing his nose up into the air, and saying, "Begone, Dog!"
But that's not what's going on. He's drawing a picture of a harried mom trying to get things done while the kids are at the breakfast table and she's focused on the wrong thing by feeding the household puppy dogs instead of feeding the kids.
And the woman to whom Jesus speaks replies, "Yes, but even when a good mom pays attention to her kids, where it's supposed to be, instead of to the puppies, the puppies still benefit from the spilled crumbs -- they don't go hungry. The mom does not actively prevent the pups from benefiting from what the kids drop."
That word "little" (such as seen in Young's Literal Translation) makes a substantial difference in how our brains draw up the picture, doesn't it?
For those who are curious, the Greek word is word #2951 in Strong's Concordance (http://concordances.org/greek/2952.htm):
kunarion: a little dogOriginal Word: κυνάριον, ου, τό
Part of Speech: Noun, Neuter
Phonetic Spelling: (koo-nar'-ee-on)
Short Definition: a little dog
Definition: a little dog, a house dog.
Cognate: 2952 kynárion – properly, puppy, a diminutive of 2965 /kýōn ("dog").
We would do well to be teaching Biblical Greek and Hebrew in our Sunday school classes, to our little ones who have the absorption capabilities to learn new languages. Within a generation, we'd have a church membership which is much more Biblically literate than our current crop of Christians.