Well you're not a religious minority, so it's easy to say that you wouldn't be offended. If you've grown up being ridiculed and bullied because you're the only kid in class who Santa doesn't visit - like my husband was - you might think differently.
Frankly, I think both you and the woman were rude. Rude of her to correct the child, and rude of you to jump in with your sanctimonious lecture.
I celebrate Christmas but unless I know that someone also celebrates Christmas, by either being someone I know personally or because we are at, say, church, it's no skin off my back to be courteous and inclusive and wish "Happy Holidays" instead.
But go ahead and keep offending people in the name of Christianity. Very spiritual of you...
ETA: for the love of God really, you see it as "oppressing" your beliefs that people think it's ludicrous to wish someone "Merry Christmas" 27 days before the actual holiday? News flash - Christmas begins in the evening on December 24. Christmas season is 12/14 - 1/6. Wish anyone you want Merry Christmas *on the actual holiday* or, if you know someone celebrates Christmas and you won't see them on Christmas, then go with "have a Merry Christmas." Other than that, it's truly "happy holidays" to be inclusive of all of the rest of the holidays that happen during this season. If you really want to stretch out Christmas in the "reason behind the season" way...wish people a Happy Advent. Oh but that would be weird, right? That at least would be seasonally correct.