I am no study of linguistics, it is an hobby, so certainly nothing I know about in depth, but this one I do find puzzling. I understand that sometimes sounds change, this happens in English today due to pronunciation and written form diverging. But what it is this that I find interesting is how often particular words across Germanic languages seem to develop in the same direction.
A good example is the possessive determiner.
*In English, they are my/mine and in both, the believed /i/ vowel has shifted first to /ɨ/, most likely, then finally to /aɪ/ today, but in some accents it has become a form of /a/, like in the American Southern accents.
*In Scots, English /aɪ/ corresponds to /a/ like in the American southern accents.
*In modern High-German, the possessive pronoun mein- also has evolved in this same pronunciation, even unto a vowel similar to either an /a/ or /ɛɪ/.
*I am unfamiliar with Low German dialects and accents, but it seems to be that for some the possessive pronouns can have any of /ɪ/, /i/, or something like /ɪˑə/.
*In Dutch, if I am not mistaken, mijn is pronounced as /m.n/ and mijne is pronounced as /mɛɪnə/. Not the same, but very similar.
*I have never personally heard West Frisian, but I am awares their possessive pronouns are spelled with a in their writing system, which should mean it is either pronounced as /i/ or /ɛɪ/.
I am probably not one to be forming opinions on this topic, but I would think that the common language from which West Germanic languages developed either used one of these vowels or diphthongs: /ɨ~ɪ̈~əɪ̈/ at least somewhere in that area.
If anything, this is food for thought.