Look at south park, family guy, 19th century cartoons of the French in English newspapers, "Bush is stoopid"-humor etc. It's funny because it's cheap and oversimplified. "Bush is relatively intelligent, but has some questionable qualities and policies" just doesn't pack the same satirical punch.
And of course precisely because it's so cheap, it's easily dismantled, so anyone who disagrees with the satire will shrug it off, find it un-funny and say: But that's not the way it is at all.
So yes, I can see several reasons why you don't find it funny, FL. (And your link made it's humor quotient drop quickly as well, CzeCze. Identifying with the girl takes the fun out of it.) But the important thing isn't to find it funny, but to understand why other people CAN find it funny because they have a different background. And realizing that you yourself find cheap shots funny that others might find "wrong". (Which I see that you do, FL.)
As for the pic itself, it surfaced around the beginning of the Iraq war, I think, so I'm guessing it's a product of modern photoshopping and modern anti-war sentiment, and not a child of the 1970's. I guess they figured the distance in time made it less distasteful while the message was just as relevant.