I think I understand the problem here. Carefully tasting coffee is something you can and should do all the time; cupping coffee is a very narrow and specialized procedure. Let me sharply distinguish the two and deromanticize formal cupping
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full cupping protocol includes precise grading, roasting, brewing, and scoring standards. It is a quality control and inspection procedure designed to compare different lots of green coffee from the same origin.
Light roasts: Since buyers know what darker roasts from each origin and varietal taste like; they cup at light roasts to exclude fermented or unripe lots, and occasionally to find the star lot.
Open Bowl Cupping, Slurp and Spit If you want to drink lots of different coffees at once, it's easiest to brew them open bowl style. If multiple people are tasting, it's more sanitary to use a spoon than to drink from cups. If you are sampling dozens or even hundreds of cups, you need to spit, not swallow.
At the SCAA cupping pavillion, a flight of coffee is attended by six to eight cuppers. Five cups each of four to six different coffees are brewed. The protocol requires tasting all five cups of each coffee to judge uniformity (although it's pointless here, since these are auction and competition coffees and won't have flaws). This procedure is repeated over the course of one to two days, until each judge has tasted the 25 to 30 submissions.
At the New York Coffee Exchange it's a lot worse: the five cup scenario is repeated for hundreds of coffees each day, and the board graders have to take thousands of slurps and spits each day. On the other hand, they only have to grade each coffee as a yes or no, not on a 0 to 100 scale.
Public Cupping Events So you see, there is nothing very romantic or mysterious about cupping; it's the only viable way to get a mostly tedious inspection and quality control procedure done. When a cafe serves their coffees cupping style rather than just handing out them out in sample cups, they are not cupping, they are having a publicity event.
Cupping at Roasters Larger and more professionalized small roasters have cupping labs -- an area with a sample roaster, a cupping table, and cupping supplies -- and they use it for several purposes. The first is to buy green coffees, where they will use their version of a full cupping protocol. The second is to create blends, and production roasts, where they will brew different roast levels of different coffees, and use eyedroppers or other measuring devices to try out different blend proportions. The third is QC on their production roasting, where they cup a sample of each production roast against a reference to make sure it's right.
Whereas formal cupping is silent, and each grader rates independently; cupping at roasters is much more convivial and relaxed, with people sharing their opinions and trying to come to a consensus. The most successful labs use the old university seminar trick of starting with the most junior person at the table and working up to the most senior, so that everyone can speak without being intellectually bullied or overborne.