Interpretation of colors, graphics, and visuals is one of the most difficult things to argue. One man's (or woman's) work of art is another's appalling wall splat. When dealing with customers, you have to realize that the art may or may not have come from a beloved genius savant daughter, son, or relative who is the creator's gift to the world.
As in Hawkgirl's explanation, the only argument you can *safely* pose here is basis in factual documentation: color theory, legibility, association, W3C color/contrast recommendations. "Because it's ugly" will get you a fast track to the door.
Sometimes you will get "I don't know art, but I know what I like," in any case; graphics, layout, design. "I want it to be alive, add some animations, it shouldn't just sit there." In these cases, you just have to make your recommendations and back out: "He/she who has the gold makes the rules."
The justification here, if you know your field and know the value of your work, is that you offered your services, and when they call you in a year blaming you for no web site sales and no visitors, you have documentation of your recommendations that were ignored because they heard what they wanted to hear.
"Do you want to make sales?"
"Of course we do."
"Understand that people come to your site looking for something, hopefully your product. If they don't see that they can find what they are looking for within three seconds, they are gone and will never return. The job of your main page is to hook them in. If they are looking for widgets, they don't care who you are, how long you've been in business, how important you are in the industry, all they care about is finding their widget. Do you want to risk losing them because you feel company history is more important than hooking them in?"
Reactions to this range from surprise and acceptance to complete rejection: "I know my customers and I know what they like," in which case you tried and they need to learn the hard way.
One last bit of advice: center yourself. You (rhetoric you, or I !) are not the creator's gift to the Internet either; always consider your design and artistic contributions are important, but not the most important thing. This is a hard pill for designers and developers to swallow. Making a site successful does not rely on design alone; people don't come to ooh and awe at graphics, they come to solve a problem. Too often projects get hung up over design when design is not the problem. Examples to demonstrate my point are this site or craigslist.org: successful beyond expectations and minimal designs. It's not always about design, so don't hold on to this too closely.