After Bnei Yisrael are commanded (reminded) not to consume the blood of an animal, Moshe provides a strong incentive to listen:

‘לֹא תֹּאכְלֶנּוּ לְמַעַן יִיטַב לְךָ וּלְבָנֶיךָ אַחֲרֶיךָ כִּי תַעֲשֶׂה הַיָּשָׁר בְּעֵינֵי ה
Do not eat it [blood] so that it may go well with you and with your children after you, when you do that which is right in the eyes of Hashem. (Devarim 12:25)
The Kli Yakar picks up on the specific inclusion of it being good for “your children after you”, by avoiding consumption of blood. He explains that the many commentators learn that consuming blood causes cruelty to develop within the person who consumed it. [One possible source I found for this is the Ohr HaChaim in Vayikra 17:10-11. There, the Torah tell us not to eat the blood of animal because the blood is the soul of the animal. The Ohr HaChaim says that when we eat the soul of animal, so to speak, we become more animalistic, taking on the traits of the animal’s soul. We lose parts of our humanity. The punishment is kareit because we are “cutting off” the human spark and cheilek elokah mi’maal and replacing it with the nefesh ha’behamis.]

The nature of a father (parent), flows into and can get passed down to children. Therefore, the Torah says that avoiding blood will be “good for you and for your children after you” so that the terrible trait of cruelty does not flow from you into future generations.

There only 2 other times in the Torah that the exact language is used of  יִיטַב לְךָ וּלְבָנֶיךָ אַחֲרֶיךָ 
One is in Devarim Perek 4:40 after summing up all the goodness and miracles Hashem performed on behalf of Bnei Yisrael, and the importance to love Hashem and follow His mitzvot. The other, is just 3 psukim after the passuk quoted above in this week’s parsha; immediately after prohibiting the consumption of blood, we are instructed about the correct way to bring sacrifices i.e. bring the sacrifices and sprinke the blood on the alter (instead of consuming it). The summary of the section is, again, לְמַעַן יִיטַב לְךָ וּלְבָנֶיךָ אַחֲרֶיךָ

The full section inside:

‘כה לֹא תֹּאכְלֶנּוּ לְמַעַן יִיטַב לְךָ וּלְבָנֶיךָ אַחֲרֶיךָ כִּי תַעֲשֶׂה הַיָּשָׁר בְּעֵינֵי ה
‘כו רַק קָדָשֶׁיךָ אֲשֶׁר יִהְיוּ לְךָ וּנְדָרֶיךָ תִּשָּׂא וּבָאתָ אֶל הַמָּקוֹם אֲשֶׁר יִבְחַר ה 
כז וְעָשִׂיתָ עֹלֹתֶיךָ הַבָּשָׂר וְהַדָּם עַל מִזְבַּח ה אֱ-לֹ-הֶיךָ וְדַם זְבָחֶיךָ יִשָּׁפֵךְ עַל מִזְבַּח ה’ אֱ-לֹ-הֶיךָ, וְהַבָּשָׂר תֹּאכֵל
כח שְׁמֹר וְשָׁמַעְתָּ אֵת כָּל הַדְּבָרִים הָאֵלֶּה אֲשֶׁר אָנֹכִי מְצַוֶּךָּ לְמַעַן יִיטַב לְךָ וּלְבָנֶיךָ אַחֲרֶיךָ עַד עוֹלָם כִּי תַעֲשֶׂה הַטּוֹב וְהַיָּשָׁר בְּעֵינֵי ה’ אֱ-לֹ-הֶיךָ 

Perhaps somewhat allegorically, the Torah is highlighting the importance of the examples that parents set for their children. A parent’s tremendous influence can either have incredibly positive or disastrously negative outcomes. If a parent has cruel traits – whether it be from literally consuming blood (unlikely these days) or simply not keeping his/her anger and emotions in check – then, as the Kli Yakar notes, that can easily, and tragically, be passed down to a child, whether intentionally or not. Assuring that we don’t have such traits will be good for us and for our children

On the flip side, if a parent has the traits of loving Hashem and demonstrating thanks to Hashem for all the good He has provided, then that example will hopefully be seen and emulated by that parent’s children. The root of the Hebrew word for sacrifice – korban – is ק.ר.ב. , which means ‘close/near’. The closeness that a parent strives to achieve with Hashem and cherishes with Hashem, will hopefully be a path adopted by the child, bringing richness and goodness to the parent, child and future generations to come.

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