To say something is 'not your cup of tea' is to say it does not suit your preferences — politely but clearly. It is a gentler way of expressing dislike or disinterest than saying something is bad or unappealing. 'Opera isn't really my cup of tea' allows you to express disinterest without implying the thing is objectively unworthy. The phrase is characteristically British in its indirectness.
Tea became the dominant British drink during the 18th century, when imports from China and later India made it affordable across the social classes. By the 19th century, tea was the drink most closely identified with British domestic life and social ritual. 'My cup of tea' meaning 'the thing perfectly suited to me' emerged naturally from this cultural centrality — tea was what you wanted, what you expected, what was right.
Interestingly, the positive form came first. 'That's just my cup of tea' — meaning something ideal for you — appears in early 20th century British print. The negative 'not my cup of tea' followed, providing a polite framework for expressing the absence of that fit. Both forms are still used, though the negative has become the more common of the two in modern British English.
No — it is considered one of the more diplomatic ways to express dislike. It signals personal preference rather than objective fault, which avoids directly criticising the thing or the person who recommended it. It is quintessentially British in its politeness.
American English uses 'not my thing' or 'not really for me.' Australians often use 'not for me' or 'not my sort of thing.' The tea-specific version is distinctively British and signals both cultural identity and characteristic understatement.