Cause Vivec killed his previous incarnation or because Vivec is a False god, or because Vivec pissed off Azura who is pretty much Nerevar his patron saint, and helped the Nerevarine a lot, because the Nerevarine wants to kill three gods instead of two, because the Nerevarine does not like the way he looks, because the Nerevarine read the 36 lessons and is jealous of Vivec his relationship with Molag Bal...
Who knows? There could be a million reasons. Personally I think the last I listed is the most likely, but you can never be entirely sure when it comes to legendary beings.
I think any Nerevarine that read the 36 Lessons of Vivec like he/she was supposed to would not hold any ill will toward Vivec. That said, my Nerevarine
did kill Vivec, but she did it with love, to reach heaven by violence, and to pave the way for his Second Coming.