Why is quote attribution important?
There are some probably quotes that everybody thinks they know, and everybody is correct. Unfortunately, I could not think of a single one, because most of the famous quotes that "everybody knows" are consistently WRONG, either in their content or in their attribution. This is especially difficult in the day of the internet because blog and article writers often assume they know the quote and do not look it up themselves, or worse, they quote a completely separate article or blog that ALSO got it wrong. This drives me nuts, and I know I am not alone because many friends have sternly warned me that I better get the quotes right. I try to find the original source material for quotes that I use - I find a text of the book, speech, or even a recording. This means that if someone brings up a question on a quote that I use, I can literally turn to a source and say, with fair confidence, "THIS is where I found it, and that is how I know."
The same thing happens with art, sometimes - especially public domain art. I found a beautiful painting I wanted to use on a shirt. The painting was included with works be Edgar Degas, but it was not quite right. No matter how many times this painting kept coming up, it was not quite right and I kept seeing different artist renditions of it (kind of like a band doing covers of another band's songs). Finally, I had to go to the actual Degas collection and this one painting was not included - hence, the Degas scholars were telling me that it was not his. Therefore, I do not know the correct attribution, and cannot use the painting as I do not know anything about the rights.
So there are 2 largish reasons there why proper attribution is important - 1) to make sure that things are as correct as possible just for the sake of being correct and not looking like an idiot who can't research adequately and 2) making sure that the copyrights of art and literature are being adhered to so that creators get their fair credit. Of course, there will be people who will (wrongly) try to argue with me, and you, just because they can and about anything, but we can't really do anything to prepare for those people except understand that they exist.