Most of your existing holidays move around every year, too. Christmas, New Year’s Day, July 4 - most of the rest move every year, right?
Pick the right thing to criticize.
Before Muhammad, the Arab calendar had intercalary months like other lunar calendars--every second or third year there would be a 13th month in order to keep close to the solar year. Muhammad thought his enemies had manipulated the calendar against him so he declared no intercalary months.
If Muslims want that kind of calendar, fine, but I'm not in favor of making everyone else celebrate their holidays.