The answer to this question can be found in chapter 1, paragraph 2. Max explains that unnamed people call him "Kicker" because he had a tendency to kick anybody at day care that tried to touch him. He is especially averse to hugs.
Called me Kicker for a time – this was day care, the year Gram and Grim took me over – and I had a thing about booting anyone who dared to touch me. Because they were always trying to throw a hug on me, like it was a medicine I needed.
Gram and Grim are Max's grandparents, and they are taking care of Max. Max's father is in jail for murdering Max's mom. Max witnessed the traumatic event, so it only makes sense that caregivers would want to give Max hugs like medicine. It also makes sense that Max responds with violence. He's young, and he doesn't understand how to properly release his pent-up emotions. Max is aware of his kicking actions, and he makes games about it.
Instead, what happened, I invented games like kick-boxing and kick-knees and kick-faces and kick-teachers, and kick-the-other-little-day-care-critters, because I knew what a rotten lie that hug stuff was.
A bit later in the chapter, Max seems to indicate that he has kicked just about every single person and kid in his class except one. Max tells readers that he could not bring himself to kick Freak.
Maxwell Kane went by many nicknames: Mad Max, Max Factor and Maxi Pad, "until I persuaded him otherwise." Because of his size and temperament--not to mention the notoriety of his father with the fearsome nickname, Kenny "Killer" Kane--it was inevitable that Max would have another moniker pinned upon him. "Kicker" was yet another of the nicknames he received. It was the name he went by when he first met Kevin in day care. Unsurprisingly, Max was called "kicker" because he liked to kick--and hated sympathy.
I had a thing about booting anyone who dared to touch me. Because they were always trying to throw a hug on me, like it was medicine. (Chapter 1)
He was proud of his nickname, and he "invented" different kicking games that included "kick-teachers and kick-the-other-day-care-critters." He believed the "hug stuff" was a "rotten lie"--a way to show sympathy for the big kid whose mother had just been killed before his eyes.
Of course, there was one later nickname that he loved above all else: "Freak the Mighty."