He says that with Alduin gone, the other dragons will bow to rightness of his Thu'um. And they will hear it whether they like it or not.
It's true that for thousands of years, Paarthurnax has taught the Way of the Voice(Which is technically a human concept, not his own) which is a way of peace, but the words of power in a Dragon's name embody who and what they are, and Paar's is Ambition Tyranny/Overlord Cruelty. Which could very well describe an ulterior motive.
Ambition - Paarthurnax wants to take Alduin's place as overlord and leader of the Dragons.
Tyranny/Overlord - When this happens, his rule could very well be worse than Alduin's
Cruelty - He's betraying and robbing and killing his own elder brother, which is a very cruel thing to do.
Also even Paarthurnax himself warns the Dragonborn that the Blades are right to mistrust him.
So his whole adopting the way of the voice, and owning up to the nature of his kind could just be a ruse to keep the Dragonborn from suspecting his plans, and keeps the Graybeards loyal to him and literally gives him a shield(cant get to the top of the mountain without going past four extremely power masters of the voice.)