Sod the teacher! Music's for enjoyment - I'll probably be excommunicated from Mudcat for preaching such heresy! - so stick with what you enjoy!!Seriously, as I've always told my pupils, playing fast is easy - it takes an expert to slow down. When you play fast the listener often cannot hear the mistakes, which you inadvertently reinforce through practice.
Only play a tune fast if you can slow it down in a controlled way whilst playing (though not in a session, just when practising!).
There's no real 'right' or 'wrong', it's down to preference, and everybody has different preferences for different reasons.
That's what makes the world go round...