A surprisingly heated seminar
One person likes plates in precise rows. The other favours what might generously be called an improvisational approach. Before a mug becomes evidence in a wider case, separate practical constraints from personal preferences.
Ask what the system is for
Water needs to reach surfaces. Spray arms need room. Delicate items need appropriate care. Those are functional considerations. The exact aesthetic of the top rack may be negotiable. Discuss the outcome you both want instead of declaring one person naturally competent and the other a permanent apprentice.
Teach once; do not supervise forever
If you genuinely do not know how an appliance works, read its instructions. Ask a focused question if necessary, then take ownership. Deliberately doing a task badly to avoid being asked again is not a charming personality trait.
Finish the cycle
An unloaded dishwasher may reduce friction more effectively than winning a debate about forks. Agree a rhythm, replace supplies and put things away. Both people deserve a home they can use without constantly chasing the other.
A modest peace agreement
Try a week with clear ownership of the full cycle. Adjust together afterwards. Your mugs do not need a parliament; your household may simply need an arrangement that is understood and followed.