If you focus on the meaning of the color Red in addition to the symbol of the ribbon, it is easier to explain why wearing the Red Ribbon is more than just showing sympathy with those affected:
The Red Ribbon is ...      

•  red like love, as a symbol of passion and tolerance towards those affected.
• red like blood, representing the pain caused by the many people that died of AIDS.
•  red like the anger about the helplessness by which we are facing a disease for which there is still no chance for a cure.
•  red as a sign of warning not to carelessly ignore one of the biggest problems of our time.