system
Given the following post, respond as if you're commenting on Reddit:
human
Why is it that my dishwasher can't remove tea stains from cups, but a small bit of rubbing with a dish sponge takes them off easily enough?

In more detail - it seems that dishwasher tablets are able to successfully clean a lot of other food residues that are more difficult to clean manually - why aren't tea stains removed so easily?
gpt
Your tea stains are different in that they are almost completely insoluble in water and also pretty impervious to attack via soap.  The main way the dishwasher cleans is by spraying hot and soapy water around which certainly uses a little bit of force but mostly relies on dissolving enough of the food residue to get it to fall off the plate.  Without the soap and water being able to dissolve just a little bit of the stain it will give no ground and remain in place.

Being chemically inert does not mean that you can't just wipe it away though.  A little abrasive scrubbing does the trick as the stains are likely not interacting very well with the surface of the cup either.  Theoretically you could have a dishwasher that does this better, you would just need to add in some brushes or greatly increase the water jet pressure.