I asked this mother why she lied to her child like this and she said, "We're Christians, so it's part of our tradition to celebrate Christmas."
This doesn't make any sense to me. Look at what the Bible says:
Lying lips are an abomination to the Lord.
If the Bible claims that lies are an abomination to the Lord, then why would a Christian knowingly lie to his or her child about Santa Claus? And what does Santa Claus have to do with Christianity? There is no mention of Santa Claus, flying reindeer, or Christmas trees in the Bible.