Dear Rich: We would like to spoof the Pittsburgh Steelers 'Terrible Towel' with a "We ARE Terrible Towel" for the Detroit Lions. It would be white with no logos. Satires can't infringe copyrights can they? Thoughts? If you're making one towel to hold up for the TV cameras, you're probably okay. But if you're thinking of making more than one, the Dear Rich Staff would advise against it. First of all -- it's not a copyright issue as copyright doesn't protect short phrases or individual words.
It's a trademark issue. The term "Terrible Towel" was created by Pittsburgh sportscaster Myron Cope who acquired trademark rights and then assigned the registered trademark to a charity, the Allegheny Valley School, an institution for the disabled. Considering that licensing revenues from the towel have earned the school over $3 million, the school and the Steelers (who acknowledge that the towel is one of the most popular merchandise concepts in football history) both have a vested interest in preventing others from making and selling Terrible Towels. It could infringe and dilute a world-famous mark (and one that is carried to the far corners of the earth.)
Does satire matter? We must clarify one thing: you stated that satires can't infringe copyrights. That's not correct. A parody may be excused as a fair use under some circumstances. The same is not always true for satires. Here's a lawyerly explanation of the distinction. In any case, your use does not seem to qualify as either a satire or a parody, does it? Bottom line: sales and distribution of your towel will likely trigger a cease and desist letter.