First of all, your teacher sucks... the man is one-sided, he's teaching you what works for him, and not for you. Teacher should adapt to a students' needs. You better quit him and do lessons with Pebber(it's not Pepper, don't insult the man) while you can afford lessons. My take on this would be, if you have two choices, use them both. It depends on how long your(or your teacher's) fingers are, and how low/high you hold your guitar while you're playing, and it depends what the heck you are about to do with your playing.
Mini barre also depends on your finger shape. If your fingertip is too wide, you can hold two strings with the tip of your fingers that have bigger diameter, and play freely major six chord shape for example, where you barre two strings with the ring finger. With pinky, for most people, it's part of pinky tip plus additional flesh from damn finger, nobody's hand is the same. For power chords, if you expand it with major third on a second string, to make a major chord, it should be index on the root, and "banana" done with the ring finger on the fifth, octave, and the third on a second string, all by that one finger.... or with second, middle and ring, if you feel more accommodated to that style. I suggest practicing doing both.
But power chords with only two fingers can be played with only two fingers, on just two strings. You can do it with single finger, if your root is higher than the fifth, or you can do it with your index and middle, or much popularized index and pinky... and you can even go with index and middle... and for some people's thinking, advanced approach with second and pinky.
Here's a little experiment... do a G power chord with your second finger on the 6th string(the root) and pinky on the 5th string(the fifth), and after that do an E power chord with open low E on 6th string(the root) and index finger on a second fret of an A string(the fifth)... try exchange these power chords for a while to see the effect. It might be weird in beginning, but you'll get the idea, and if you like it, you'll use it. It's popular to call this mechanics as "spider chords" or better to say, "spider power chords", and I believe Dave Mustaine from Megadeth coined the term, even it's been on the market before him.
To summarize, if you have two, or more choices, do them all and find what approach match your style the best... there's no definite rule that could accommodate different traits of anybody's anatomy.