Which garbage can is up or down?
An ASL student confidently signs garbage can only to be corrected by a ASL instructor or ASL speaker. The student at first was puzzled, momentarily thinking "How can it be incorrect?"
If a small phonological part of the signed word is altered or mispronounced, it can result in a different meaning, simply a "misspelling", or meaningless. Even the slightest difference can mean something different.
The downward movement from the top of the ASL sign garbage can is mispronounced. The movement should be upward from the bottom. Oh, another error is that the handshape should be "C", not "baby C".
Why? Well, it's a language of its own. Every language has its phonological-morphological rules.
Likewise for the ASL sign building. The movement should be upward from the bottom. And the handshape should be full "C".
What else can you think of other containers and related signed words, in which the movement is upward from the bottom? One example is bottle.
It's a whole different story for cup. The movement should be downward from the top. And, the movement is twice and short.
No need to memorize these phonological rules. We don't think of these rules. It's just natural in language acquisition without really thinking about them.
Also see co-articulation in sign language