These arguments justifying dishwashers are silly. How expensive is your water that this small saving is going to offset the cost of electricity and the appliance itself? You use a dishwasher because you're lazy, not because of efficiency or cost benefits. It's OK to just say. I hate washing dishes too.
1.5 hours a day and a high water bill is a ridiculous exaggeration, though. Like with anything, the more you do it the better you get at it. I wash dishes currently because I don't have a dishwasher. It takes 10-20 minutes tops, and my water bill is lower than my internet bill (and much lower than internet + various media subscription services that I don't need).
It’s not just laziness or cost. Dishwashers use less water than manual washing. Clean water is a scarce resource.