I can’t stand him.
Ich stehe auf ihn.
These two idioms using the word “stand” or stehen communicate very different feelings about another person. In the English case, if you can “stand” someone, then you can bear to be with her/him, although you probably aren’t particularly keen on this person. If you “can’t stand” someone, you really don’t like her/him and/or cannot bear to be with him/her. In the case of the German colloquial expression auf jemanden stehen, you are “keen on” someone or you “have a crush on” him/her, “a thing for” her/him, you are “into” him/her or you “fancy” her/him. In addition to sharing your likes or dislikes of other people, both expressions can also be used to describe feelings about the things you don’t much like (English) or like very much (German).
Both stehen and “stand” seem to be pretty productive. In German this productivity is found in the compound words made from stehen or its relatives. Standhalten — stand is a relative of stehen — means that you can “bear up under the pressure” (den Druck standhalten), “hold your own” (wacker standhalten) or that your ideas can ”withstand” scrutiny (einer genauen Untersuchung standhalten). Stehen also appears in the prefixed verbs ausstehen, durchstehen and überstehen, all of which have to do with “bearing, enduring, withstanding, weathering or surviving” something.
In the case of English, the productivity flows from collocations between “stand” and prepositions and the idiomatic uses of the verb. Thus, you are not likely to “stand up for” someone (einstehen, entreten, verteidigen) you can’t stand, nor would you be willing to “stand” this person a drink (spendieren), you probably don’t like what they “stand for” (für etwas stehen) and there is quite possibly something that “stands between you” (≈dazwischenstehen), making it difficult for you to get along. And I must confess (gestehen) that I giggled at the possible confusion that might ensue from the sample usage given in the Cambridge dictionary’s definition of the idiom “to stand on ceremony” (to behave in a formal way) because the literal and figurative meanings of “stand” both appear to be relevant — “Please sit down and make yourself comfortable, we don’t stand on ceremony here.” I guess they don’t want to leave their learners “upstanding.”