Athens - How could Athens preach the virtues of democracy, but still allow slavery?

How could Athens preach the virtues of democracy, but still allow slavery?

I've got a project to do on Athens and Sparta, so please make sure that it's the right answer.

Because the democracy that Athens practised was not democracy as we know it today.

Now - how do you know if this is a right answer or not ?
Athenians believed the nation should be run by CITIZENS, not just humans. We believed the same thing in the Southern US before the Civil War. All the guys who invented and defined American democracy were slave owners.

Aristotle wrote something about this. (I was just looking for it on Google but couldn't find it. Maybe you can). Ari felt that a real 'man' should not have to work because work takes up all his thinking. A real man should have leisure time to think about things, to come up with thoughts and ideas. Work was for slaves, people with less intelligence.

In America (and other western countries) we think of work as somehow ennobling. We call this 'the work ethic'. But people didn't always feel that way. The Greeks thought rich people with leisure time were smarter and wiser, and therefore -they- should be the ones who voted and made decisions and ran the country.
Is the quote, "All paid jobs absorb and degrade the mind."?
. . . just shows you: Democracy = demon crazy!!! LOL!
Greek democracy was direct democracy. Greeks would, without hesitation and without exception, regarded all our representative democracies as oligarchies. The crucial issue is that how the vote is taken is decided not by the assembly of citizens but by the elected council.