Why did Sakura think she could kill Sasuke alone? Was it out of love or a sense of duty?

True strength is defined not by the power to destroy, but by the capacity to endure pain for the sake of others. Discussion Points for Study

Look for the contrast between the cold, snowy environment of the bridge and the "heat" of Sasuke’s rage.

Sakura finds Sasuke, who has just defeated Danzo and is consumed by hatred. She claims she wants to join him, but Sasuke tests her resolve by demanding she kill the injured Karin.

Sasuke's burden is the "curse of hatred" from the Uchiha clan, while Naruto’s burden (introduced shortly after) is the choice to absorb that hatred to stop the cycle of violence.

Kakashi exemplifies the burden of leadership. He views Sasuke’s descent into darkness as his personal failure.