Claim: The term 'Xmas' is a modern, disrespectful abbreviation of the word 'Christmas.'
Origins: The abbreviation of 'Xmas' for 'Christmas' is neither modern nor disrespectful. The notion that it is a new and vulgar representation of the word 'Christmas' seems to stem from the erroneous
belief that the letter 'X' is used to stand for the word 'Christ' because of its resemblance to a cross, or that the abbreviation was deliberately concocted "to take the 'Christ' out of Christmas."
Actually, this usage is nearly as old as Christianity itself, and its origins lie in the fact that the first letter in the Greek word for 'Christ' is 'chi,' and the Greek letter 'chi' is represented by a symbol similar to the letter 'X' in the modern Roman alphabet. Hence 'Xmas' is indeed perfectly legitimate abbreviation for the word 'Christmas' (just as 'Xian' is also sometimes used as an abbreviation of the word 'Christian').
None of this means that Christians (and others) aren't perhaps justified in feeling a little miffed when people take the shortcut of writing 'Xmas' rather than 'Christmas,' but the point is that the abbreviation was not created specifically for the purpose of demeaning Christ, Christians, Christianity, or Christmas: it's a very old artifact of a very different language.