Airports are still pretty busy on Thanksgiving day and some people still fly someplace on Thanksgiving day so that makes the Airports pretty busy on Thanksgiving day.
However most people who fly for Thanksgiving day fly the day or a few days before Thanksgiving day.
They fly a few days or a day before Thanksgiving day to get to the destination and be at families homes etc before Thanksgiving day.
So flying on Thanksgiving day would mean that the airports are less busy than they are the days leading up to Thanksgiving day.
Even the days after Thanksgiving day are pretty busy because the people are flying back home.