One year back in high school, one of my classmates who was very religious gave everyone candy canes with a message on it. It was about the origins of the candy cane and what it symbolizes. Was indeed the candy cane created to be 'J' shaped for Jesus? Was it true that the white represented Jesus' purity and the red is blood sacrifice? Uh....no. My research tells me that candy canes were originally candy sticks without red in them. I became popular to add red and other colors during the early 20th century. There may be some truth to them being bent into shepards' crooks, but no one is entirely sure if that's true either. So while it may be nice to use them as a teaching tool, there is no evidence to support the fact that they originated as one.
So too is the 12 days of Christmas song another falsity. I've seen postings and read e-mail where it's origins are that it's an English carol devised by Catholics to teach the catechism during the time where Catholics could not freely practice their faith. It's not. For one thing there is no documentation to support this. Secondly, there is some evidence that the song is actually French in origin. And finally, if you look at what the claims are that the symbols mean, the Anglican's themselves would have no problem with them since they are the same for them too. So why make a carol to hide things that Anglican's would believe like four gospels and 8 beatitudes?
Although I will tell you that there is some truth that the pretzel was indeed invented by monks. Although not for teaching purposes either. And Silent Night was written by an Austrian priest by not on Christmas eve because the organ was broken. He just wrote something simple. So don't despair. Some things do have religious origins, but it's not always what the legends make it out to be.