One possible motive could be a complete breakdown of the peace they had worked so hard to build. Maybe an outside force manipulates Gaara's mind, causing him to turn on Naruto. Another could be extreme jealousy over Naruto's popularity or power.
Maybe Gaara was driven by deep-seated anger and trauma. The consequence could be a total change in his relationship with Sakura and his place in the community.
Naruto is often paired with Gaara in these fanfictions. Their strong bond in the original series makes it interesting to see how they interact when Gaara time - travels. Naruto could be the one to help Gaara adjust to a new time period or vice versa.
Often, Naruto's female characters are paired with Gaara. For example, Hinata. Since Hinata is a kind - hearted and shy character, her relationship with the initially cold - hearted Gaara could be an interesting exploration of how two different personalities come together.
Naruto could still be a main character. Their relationship would likely be different if Gaara were a girl. Maybe Naruto would be more protective of her.
It could be Orochimaru. He might manipulate Gaara into kidnapping Sakura. Orochimaru could have his own devious plans for Sakura, like using her medical knowledge for his experiments. So, he uses Gaara's power and his somewhat unstable mental state at times to achieve his goal. Then Sakura and Gaara would have to team up to fight against Orochimaru.
It's a complex situation. Different storylines and villains have targeted the Avengers, but no one specific character can be said to have killed them all outright.