idiom-meaning
"It's not my cup of tea" means something isn't to your personal taste or preference, using tea — central to British daily life — as a stand-in for anything one might or might not enjoy, and it's commonly used to gently decline an activity or express mild disinterest without being harshly negative.
"I have no tea" is a literal reading that misses the idiom entirely, and "I'm busy" describes availability rather than preference — neither captures the actual meaning of politely expressing dislike or disinterest that the phrase conveys.
The idiom's softness is part of its charm — saying something "isn't my cup of tea" sounds far gentler than bluntly saying you dislike it, fitting British conversational habits of understatement.
Quration — Quration English