ὑμιν is the dative case of the second person plural pronoun - ie. TO YOU (pl)
It’s not pronounce hoo-min except in seminaries where the Erasmian system of pronunciation is still predominant - pronunciation that was never used by real people, but makes the grammar clearer and more analogous to Latin. Actual pronunciation in the Koine Greek period and in Modern Greek is ee-meen - the aspirate is not voiced and many vowels and diphthongs had tended to “i” in pronunciation by the post-classical period (Iotacism).
Resemblance is not etymology: “human” in English descends from the Latin “humanus.”