[Dylrob]

Given the contradictory nature of English genitive case (ie possessive), I find it easier to just associate the ‘ with contractions.

Of course it also helps that I know that ' originally stood for an omitted vowel. Hence ’Twas (It was). The reason its used most of the time in English genitive case is because the ending used to be “es”. (That said, plurals also used to end in “es”, regardless of the word, and in fact you see the ‘ being used to substitute this missing e in old manuscripts as well)