Are you listening to me?

If a person appeared to doze off in your presence, you could feel fairly certainly he wasn’t too interested in what you were saying. What would be rude in a human being isn’t at all rude in a cat, however.

A cat settling in your lap or nearby who half-closes his eyes isn’t showing a lack of interest; rather, closed eyes imply total trust and relaxation. (And whether you’re saying something fascinating or boring doesn’t much matter to the cat anyway.)