可是
kěshì · HSK 2
but
可 (can) + 是 (is) = 'can be... but'; a soft pivot word
可是 literally stacks 可 (may/can) with 是 (is/yes), giving a hedged 'it may be so, however...'. Functions like English 'but' or 'however' to introduce a contrast after a concession.
可 — mouth 口 + breath marker 丁 (modified)
可 originally depicted a mouth (口) with a curved stroke suggesting exhaled breath or speech, conveying approval or assent. From this came the meaning 'to permit' or 'can,' as granting permission was expressed verbally. Today it broadly means 'may,' 'can,' or 'approve.'
是 — sun 日 + 正 (correct/upright)
Originally a compound suggesting 'the sun 日 directly overhead'—straight, correct, true. From this concrete sense of 'right' or 'this very thing,' 是 came to mean 'this' as a demonstrative, and later the modern copula 'to be / is.' The 'correct' meaning survives in words like 是非 (right and wrong).