When people say (B), they mean that Christmas is not mentioned in the Bible, nor is Christ's Birthday given a date (you'd think the Bible-writers would have had the courtesy to give the hour, minute, and second, too). Nor was Christ's Birthday important to Christians at first. Plus, the whole December 25th bit has more to do with the Winter Solstice and Saturnalia and Mithra than the Baby Jesus. And the Puritans didn't care for Christmas. Etc. All true.
Includes a lot of great christmas mp3's, (including a track "Put Christ Back into Christmas" 1950) so go check it out