I've crafted two bins full of mugs, yet I still have dwarves having unhappy thoughts about drinking without mugs.
You need an Inn or dining hall with a storage
First, you need to create an inn or dining Room.
In an Inn, add a chest/coffer, and suddenly it will start to gather mugs, cups, and other goblets to hand to its patrons.
In a Dining Hall, have a stockpile area that is only for Goblet type products.