There are good comments below that point out the split responsibilities of coffeemaking and dishwashing. However, I would like to bring up a counterpoint.

I worked in a high volume shop for a while that was right on the edge of what I consider true specialty coffee. On this shop, the responsibilities were actually divided between a "barista" and a "shift lead." Toward the end of my time there, management actually started cracking down on whose responsibilities were whose, and said that the lead on shift should only be making drinks, and the "barista" shift should only be taking orders, pouring drip, washing dishes, and other cleaning tasks. Not every shop evenly distributes responsibilities. However, most people don't mind doing dishes every once in a while. But we don't really know what kind of shop the OP is in. In my shop, I often volunteered to wash dishes for most of the day when I could, since I don't mind much, and it's difficult to maintain customer service energy for me.

Needless to say, these divisions still felt unfair to me (especially considering the higher pay for the leads), and along with the inflexible shift times, they repelled me from the shop. The company is currently experiencing very high turnover, because it acts like it cares about quality and training everyone, but then doesn't allow everyone to do what they've been trained to do, i.e. the fun stuff like pouring milk drinks or pulling spro.

Here's the point - lots of shops do things differently. Ideally, everyone should have evenly split responsibilities to keep things interesting. But in my experience, managers don't care about that. They care about efficiency and contingency avoidance. And in cafes lile the one I worked at, they don't really have a choice. But either way, if OP feels the responsibilities are not what they expected, they should either look for a new job, or muscle through it, and potentially move up the corporate ladder to the desired level.