Romney is claiming that "President Obama is running a campaign of 'hate'" and saying that "the president sought to divide Americans based on 'income, age, and ethnicity.'" Comments claiming that Romney is just 'projecting' let him off the hook for his nasty campaign methods. This is NOT a Republican psychological quirk! What Romney is doing is a time-tested nasty campaign strategy that is designed to convince voters to let the Republicans avoid responsibility and blame for the nasty statements they make about Obama.
This is a time-tested Karl Rove strategy. By accusing Obama of doing what Romney himself is doing, Romney inoculates himself from being blamed for what he is doing. He is creating a he-said, he-said situation in which blaming Romney for what he is actually doing is cancelled out by Romney's claims that Obama is also doing the same thing. Yet even as Romney inoculates himself from the nasty statements he is making, they still are being used to paint Obama as running a dirty campaign and voters register this feeling.
At the same time, Romney himself is merely let off as demonstrating a harmless psychological quirk.
Karl Rove developed this technique during Texas campaigns in the 1990's and the Republicans have used it nationally ever since.
Don't just dismiss Romney's statements as merely the wild rantings of a loser Republican. They are in fact a carefully crafted and nasty Republican ratfuck. Dismissing what he says as 'merely projection' allows Romney to win this round with the media.