This is something I harp on continuously, or at least seasonally. The holiday is established by law and the statutory name of the holiday is “George Washington’s Birthday.” Nixon’s offhand remark robbed a great American of his due observance. For the life of me I don’t know why the misnomer has caught in like it has.
Nixon’s remark was probably made out of ignorance rather than malice—he may have thought that both Washington and Lincoln were being honored (although Lincoln had never been honored with a federal holiday). Unfortunately the misnomer caught on.