A Voice from the Past - Gregory the Great

Now I confidently say that whoever calls himself, or desires to be called, Universal Priest, is in his elation the precursor of Antichrist, because he proudly puts himself above all others. Nor is it by dissimilar pride that he is led into error; for as that perverse one wishes to appear as God above all men, so whoever this one is who covets being called sole priest, he extols himself above all other priests. But since the Truth says, Every one that exalteth himself shall be humbled (Luke xiv:11; xviii. 14) I know that every kind of elation is the sooner burst as it is the more inflated.

Pope Gregory I, Epistles, Book VII, Epistle XXXIII, 597 AD (Nicene and Post Nicene Fathers, Vol. XIII, T & T Clark/Eerdmans, trans, Rev, James Barmby, p. 226)

What are the implications of this quote? Why is it important?