There are many Thanksgivings in history, and harvest is traditionally a time of thanks. Our celebration of the dinner between Pilgrims and Indians however has some really dark roots. There were those 3 days of feast, to celebrate a treaty giving 12,000 acres of land to the Pilgrims. The indians brought the majority of the food. The rest is just plain ugly. Edited for length, links at bottom.

In 1621 the myth of thanksgiving was born. The colonists invited Massasoit, chief of the Wampanoags, to their first feast as a follow up to their recent land deal. Massasoit in turn invited 90 of his men, much to the chagrin of the colonists. Two years later the English invited a number of tribes to a feast "symbolizing eternal friendship." The English offered food and drink, and two hundred Indians dropped dead from unknown poison.

The first day of thanksgiving took place in 1637 amidst the war against the Pequots. 700 men, women, and children of the Pequot tribe were gathered for their annual green corn dance on what is now Groton, Connecticut. Dutch and English mercenaries surrounded the camp and proceeded to shoot, stab, butcher and burn alive all 700 people. The next day the Massachusetts Bay Colony held a feast in celebration and the governor declared "a day of thanksgiving." In the ensuing madness of the Indian extermination, natives were scalped, burned, mutilated and sold into slavery, and a feast was held in celebration every time a successful massacre took place. The killing frenzy got so bad that even the Churches of Manhattan announced a day of "thanksgiving" to celebrate victory over the "heathen savages," and many celebrated by kicking the severed heads of Pequot people through the streets like soccer balls.

The most interesting part of thanksgiving is the propaganda that has been put out surrounding it. During the 19th century thanksgiving traditions consisted of turkey and family reunions. Whenever popular art contained both pilgrims and Indians, the scene was usually characterized by violent confrontations between the two groups, not a multi-cultural/multi-racial dinner. In 1914 artist Jennie Brownscombe created the vision of thanksgiving that we see today: community, religion, racial harmony and tolerance, after her notorious painting reached wide circulation in Life magazine.

On June 20, 1676 Edward Rawson was unanimously voted by the governing council of Charlestown, Massachusetts, to proclaim June 29th as the first day of thanksgiving.
It was not until 1863 that Abe Lincoln, needing a wave of patriotism to hold the country together, that Thanksgiving was nationally and officially declared and set forth to this day.

Adamant protests to the celebration of thanksgiving have taken place over the years. As early as 1863 Pequot Indian Minister William Apess urged "every man of color" to mourn the day of the landing, and bury Plymouth Rock in protest. In 1970 Apess got his way. 1970 was the "350th" anniversary of thanksgiving, and became the first proclaimed national day of mourning for American Indians.

For the next 24 years, American Indians staged protest every thanksgiving, in 1996 the United American Indians of New England put a stop to the annual pilgrim parade and forced the marchers to turn around and head back toward the seaside (symbolism?). In 1997 the peaceful protestors were assaulted by members of the Plymouth police, the county sheriffs department, and state troopers on horseback in full riot gear. Men, women, children, and elders were beaten, pepper sprayed and gassed. Twenty-Five people were arrested; blacks, whites, latinos, Indians, and even a 67-year-old Penobscot elder were taken to jail. Videotape was later produced to confirm the assault and ensuing police brutality. Plymouth is known as "Americas Hometown."

http://aspin.asu.edu/hpn/archives/Nov98/0380.html
http://www.2020tech.com/thanks/temp.html Recommended reading.Scroll down.
http://www.rense.com/general45/thanks.htm

Should we stop teaching our children and believing the false stories of this Pilgrim/Indian alliance and begin to aknowledge and tell the truth about it?

We should tell the truth, yes, but it is somewhat complicated when dealing with very young children, because they shouldn't be burdened with information that they might not be ready to process psychologically. The history of Thanksgiving is violent and complex. I'm not sure how or when you could effectively begin to teach it. Perhaps some of the parents on AD could give some insight into their experiences with teaching violent subject matter to children.

The way that I might celebrate Thanksgiving with my children would be to not focus on the alliance with the Indians, which we know is false, but to focus on the bountiful harvest, which is, in essence, what our current holiday of Thanksgiving is about.

When discussing the relationship between the colonists and the Indians, I would share with them that coming to the Americas presented many difficult problems, and I would initially focus on Jamestown and the "starving time" when many colonists joined with the Indians so that they would be fed. I would discuss the chilly relations between the Indians and the colonists honestly, explaining the struggle over the land and the generosity of the Indians who were willing to help people who were a part of a group that was not necessarily benevolent. I would also discuss the action of revenge that was taken by the English because the Indians refused to return the desperate settlers when asked and the subsequent war over land that followed. The story could be used as a lesson in compassion and strength of will, and I think that it could be simplified enough for a young child to understand while still casting the relationship between the settlers and the Indians in a light that is more true to reality.

As the child matured, the situation could be described in more detail, including the full story of the Thanksgiving day massacre.