Vivec did kill Nerevar, and he's killed (directly or indirectly) various Nerevarines since (remember that you're not the first, there's at least a cavern full of others that came before you).

"If there is to be an end I must be removed. The ruling king must know this, and I will test him. I will murder him time and again until he knows this. I am the defender of the last and the last."http://www.imperial-library.info/mwbooks/lessons.shtml#13

And yes, he tried to kill you too, remember this?:

"The outlaw named %PCName, stated trade of %PCClass, lately called 'Incarnate' and 'Nerevarine,' now is shown to the investigating Ordinators and Magistrates of this district to be an agent in the pay of the Imperial Intelligence Service.... %PCName is sought for various crimes by Ordinators and town guards. Report all encounters with this outlaw to the proper authorities. If you see this outlaw in public, give the alarm.

Published by the authority of the Temple...http://www.imperial-library.info/mwbooks/public_notice.shtml

Of course, he had his reasons, apart from those mentioned in the Sermons (the rest of the quote I gave before):

"Why did I try to kill you? Because you threatened the faith of my followers, and I needed their faith to hold back the darkness. And I thought you were my enemy -- a pawn of the subtle Daedra Lord Azura, or a pawn of Emperor Uriel Septim, or a simple fraud -- perhaps a Hero -- but not much of one if my faithful could destroy you. Now circumstances are altered. I need you, and you need me.--Vivec