Mi is the possessive pronoun, "my father" mí is usually prefaced by "a mí" making it a direct object and/or indirect object. IE "He threw the ball to me." Or in the case of gustar and encantar... Me gusta we translate as I like it. But really it's literal meaning is its pleasing to me. In such cases "a mí" is used at the beginning of the sentence to provide emphasis that whatever "it" may be is pleasing specifically to me.
In English most of our vowels are actually two sounds and in Spanish they are more pure. For example, in English our "No" is said more like "No-u" vs. Spanish where "No" is simply "No". No rounding out the o like we do in English. (It's one of the many ways Spanish speakers can tell if it's not your first language) So that's one possibility. Another possibility is that it sounded more like mí. And the other possibility is that it just didn't catch it. Happens to me all the time in the German lessons. If you have a lisp/stutter, it doesn't always catch it as well. Like if you are using voice to text on your phone. Also it just might not recognize your tonal sounds. Voice to text is picky that way. For example, if you have an iPhone, Siri doesn't always hear you right. Same with android's Google Assistant or if you download the Cortana app.
Yes in Spanish father is (padre) and dad is (papá)
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