I did an experiment where we needed to calculate the enzyme activity with an inhibitor using the absorbance. The question was, why do we calculate the absorbance only between 1-3 minutes of runtime and not any longer? Why did we not use the first minute in the calculation ? My teacher said it was related to the inhibitor

I do not think that this is a rule. In fact, certain reactions are way faster and hard to measure colorimetrically. I assume that it was an empirical value for your particular test. I.e. at short time frames the values are fluctuating too much, and after a minute or so it settles into a smoother curve.