지만

but, joining two contrasting clauses

Glues a concession to what comes next: 좀 이상하지만 귀여운 is "a bit weird, but cute", 팔지만 is "I sell it, but…". It is neutral about politeness — the ending that decides formality comes later in the sentence — so the same word works in a joke and in an apology. 죄송하지만 ("I'm sorry, but…") and 모르겠지만 ("I don't know, but…") are near-fixed openers for softening what follows. Compare -ㄴ데, which also links clauses but often just supplies background rather than a real contrast; -지만 always signals genuine opposition.