Grieving for the original Zari, his Zari, feels somehow wrong to Nate when there's a version of Zari on board the ship with them, even if the Cat Chat influencer Zari created in the new timeline isn't the Zari he had grown to fall in love with. Plus the Zari he loved isn't technically dead, merely returned to the totem in order to save Behrad from dying again. She still exists, but he can never see her again, and in another way, grieving her feels right.
Legends of Tomorrow, Zari/Nate