Why the root words in Latin don't match up with the months?

Yes, the names of the months match their Latin roots. January comes from Janua for the outer door of a house. February comes from februum for 'religious purification'. March comes from Mars the war god. April comes from aperire for 'to uncover, open'. May comes from Maia, the mother of Mercury the winged messenger of the gods. June comes from Iunius, as the name of a Roman clan. July comes from Iulius, as the name of the Roman clan formed by the descendants of Prince Aeneas of Dardania and Troy. August comes from Augusta, the wife of a Roman Emperor. September comes from septem for 'seven', October from octo for 'eight', November from novem for 'nine', and December from decem for 'ten'. The reason for the names of the last four months is the Roman identification of March as the first month of their year, April as the second, May as the third, June as the fourth, July as the fifth, and August as the sixth.