Due to the theme of hate seemingly set to be central to the game's story, there are a few possibilities
1) Ellie hates Joel for lying to her about the Fireflies so she wants revenge for him dooming humanity and killing Marlene. However, this appears false as the pair are seen together in the trailer; any animosity from that isn't visibly present.
2) Someone, likely the Fireflies, have created a cure but did something sinister to do so (harmed Ellie, attacked and tortured Tommy's community to gain new test subjects or, though probably the most cliche/unlikely, killed Joel). If the latter, then Joel is merely a projection from Ellie in the trailer but this feels too predictable and would hamper the story in the long run.
3) A new group has appeared and has committed a dark act, likely harmed Tommy's community, fuelling Ellie and Joel with a desire to go after them.
4) The Infected, Ellie wants to wipe them out. But this just isn't feasible, no way can she wipe out an entire species by herself.
5) Last one that comes to mind, the Infected-Humans have evolved and now maintain their human characteristics longer. This is probably my most 'creative/unorthodox' theory I can come up with. The evolution explains why Ellie is immune, plus it supports that the infection is inevitable, can only merely be delayed. Ellie hates this, making her against the cure which then links in to Theory 2/4.
That's all I've got for my expectations of hate is the main theme. Hopefully I'm incorrect with all of these so the new game really takes me by surprise.
I'm also looking forward to how playing as a 19-year old Ellie works. Be pretty cool if they mix in a few aspects from the Uncharted series; let us scale buildings/trees to some degree due to Ellie being younger and so on.
Also, I wonder if Joel's age will affect him in anyway. If we ever play as him, it'd be cool to see if he is slower, can't run as long or is still as able bodied as he was in TLOU, shifting us to and fro from the old style of play to Ellie's new format
I made that longer than intended but the above are what I'm expecting/theorising so far ^_^