As a diehard communist, he would have planted in their minds at an early age that Christmas was an "evil" thing (even many mere Libs do this). He wrote poems attacking Christianity.
Barack Obama, from Dreams from My Father, Three Rivers Press, New York, Revised Edition, 2004, ISBN 1-4000-8277-3, p. 76-7:
"But by the time I met Frank [Frank Marshall Davis] he must have been pushing eighty, with a big, dewlapped face and an ill-kempt gray Afro that made him look like an old, shaggy-maned lion. He would read us his poetry whenever we stopped by his house, sharing whiskey with Gramps out of an emptied jelly jar."
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Frank Marshall Davis
From Accuracy In Media | AIM.ORG
Obamas Red Mentor Praised Red Army
AIM Report | By Cliff Kincaid | April 30, 2008
Barack Obamas childhood mentor, Frank Marshall Davis, a member of the Moscow-controlled Communist Party USA (CPUSA), wrote a poem dedicated to the Soviet Red Army. Smash on, victory-eating Red Army, he declared. He also wrote poems attacking traditional Christianity and the work of Christian missionaries.
http://www.aim.org/aim-report/obamas-red-mentor-praised-red-army/
Woulda, Coulda, Shoulda, None of that is proof. My thinking is that whatever his feelings about religion, his kids would have been QUITE upset not to get Christmas Presents, and I doubt even he would want to hurt them so badly.