Why does max leave the Hubermanns home?

Basically because he does not want to put Liesel or the Hubermanns at any more risk. Being found hidden in their basement would most certainly have grave consequences. Max also wants to actively fight the Nazis.

He doesn't want to put the Hubermann's in more danger. The army were going to each house to check if any family's were hiding Jewish families in their homes. Max decided to leave the Hubermann's house to not get them hurt or himself killed.

If he had stayed there any longer than he had to, then he'd be put in jail or killed. Remember, this event happened during Adolf Hitler's reign of terror as he was responsible for the deaths of 6 million Jews. After everything the Hubermann's did to protect Max, he returned the favor by leaving them to keep them safe.