Why should I not wash my hair before dying it?

My box of home hair dye says that my hair should be clean and damp but not newly washed. Why? What will happen to my hair if I wash it first? Or have dirty hair? I hate dying my hair if I have spent ages styling it but if I wash it and don’t style it for a day then I have stone-age woman hair. Or if it is needing a wash and I dye it, it still needs a wash after. How dirty is dirty? Is a bit greasy ok? Will it damage my hair or scalp? My hair is tough but my scalp is sensitive. Help!