There are a few good points from the article 5 Big Usability Mistakes Designers Make on Carousels, which could give insight to what problem there might be designing carousels:
- Auto-sliding after the user has already taken control
- Displaying new items in a row one at a time
- Showing item progress in a confusing way
- Infinite sliding
- Tiny click targets
If you've been on the web for +10 years, you should also know that moving content is a bad idea. The reason is advertisement who spend a lot of time making their ad as visible as possible through bright coloring, moving images, animations and all sorts of flashing thing. The only effect that had on users of the web where that they learned to avoid movement of any kind. It's probably not as valid today, but personally I don't use carousels for that reason - it looks like advertisement.
That said, you can use a carousel if you avoid the above mentioned design mistakes and implement a style that is coherent with the rest of you web page in terms of colors, shadings and fonts. And if your customers want it ('cause the competition got it) your probably in a bit of a trap. That's why you need to make your carousel better than competitor web site AND point it out to your customer. You'll get a useful carousel and a happy customer willing to pay the invoice.