Sometimes this is how people get in trouble because it is called "the Jews' Feast of Tabernacles" here. But I think John did this under the inspiration of God. God is showing some measure of displeasure because of things the Jews were doing, the attitude they had toward the Feast, and He was kind of distancing Himself away from it here. It had nothing to do with the Jews keeping it on the wrong day, because they did keep it on the correct day. They had also added a fairly large number of traditions to the observation of the day, the most famous of which apparently even Jesus approved of, at least to some degree, because He picked up on it, and He said what He said in John 7:37.
