The title says it all:

Why is "I'm stressed and need the day off" a bad reason to take the day off? And how can I phrase it so that it would be more acceptable? I've seen this attitude at my current and previous workplaces, as well as reading on the Internet and talking with other people about their workplaces.

We use A Paid-Time-Off pool, so we just have a pool of time we can draw from, but we're supposed to give notice as far ahead of time as possible. No one else at my workplace ever takes sick days (unless they're in the hospital - I'm not exaggerating here) and the general view is that taking time off is time spent not being productive.

If I'm so stressed or tired that I'm making mistakes, how do I tell my boss this without seeming like a slacker? How do I get him to understand this will not go away with a single night of good sleep?