Questions & Answers about Я п’ю чай чашкою.
Because Ukrainian often uses the instrumental case by itself where English would use with. The case ending already shows the idea of means or instrument.
For example:
- пишу ручкою = I write with a pen
- їм ложкою = I eat with a spoon
So чашкою can express with a cup / using a cup without a separate preposition.