* Protecting her sister: The most obvious motivation for Katniss is to save her younger sister, Primrose, from certain death. Knowing that Primrose would be chosen as the tribute if she didn't volunteer, Katniss steps up to take her place. This is a clear act of self-sacrifice driven by familial love.
* Providing for her family: The Hunger Games are a cruel system where the victors receive wealth and benefits. Even if Katniss didn't win, the act of volunteering itself offers the possibility of a small reward for her family. This signifies her desire to improve their lives and protect them from poverty.
* Keeping her family together: By volunteering, Katniss is ensuring that she won't be taken away from her family completely. If she had stayed at home, she would have been forced to leave them to participate in the Games, potentially for good. Volunteering allows her to stay close to them, even if only briefly.
Important Note: While the story explores the themes of love and sacrifice, it's important to remember that Katniss's motivation is complex. She's not just driven by love but also by a sense of duty, defiance, and a desire to survive. Volunteering is a desperate act of survival, fueled by love but also by necessity.
The novel doesn't explicitly say "Katniss volunteered because of love," but her actions speak volumes. The depth of her love for her family is a central driving force in her decision and ultimately shapes her journey throughout the Hunger Games.