It's a false legend promoted by today's democratic governments.
In fact democracy in Ancient Greece wasn't how we know it today:
-It was only limited at the city of Athen
-Only adult rich men born in Athen with both the parents citizens of Athen could vote, in fact that was a minority
Most important
-People absolutely didn't like democracy, not who couldn't vote, they didn't care, but philosophers like Plato.
If you want I'll link sources in the comments, now I'm not at home.