The Boys season 1 ended with Billy Butcher at the mercy of Homelander, but at the start of season 2, he’s alive and well. The question remains: why? Considering Homelader's complete and total disregard for humans in general and his annoyance at Butcher, it seems out of character for him to just let the man go without punishment. However, the first three episodes of The Boys season 2 reveal the reason why he let Butcher go unharmed and it involves the big twist at the end of last season.
At the end of The Boys season 1, in an attempt to hurt Homelander for the "death" of his wife, Becca, Butcher took Madelyn Stillwell hostage at her own home and rigged the entire house with explosives. Butcher knew Homelander was obsessed with Stillwell and the trap might’ve worked if it wasn’t for Homelander learning Stillwell had lied about Becca’s death and the existence of his son. Due to her betrayal, Homelander killed Stillwell himself. When Butcher pressed the button to destroy the entire place, Homelander quickly flew him out of the house and took him to Becca’s home to show Butcher she was actually alive.
During the first three episodes of The Boys season 2, Homelander visits Becca hoping to form a relationship with their son, Ryan. This makes Becca extremely uncomfortable and afraid for obvious reasons: Homelander is terrifying. When she tries to send him away more forcefully, Homelander reminds her of the deal they made: he keeps Butcher alive and she lets him see Ryan. While he calls it a deal, Homelander’s powers and sociopathic personality make it more likely that he’s using Butcher’s life to keep Becca in line. In the end, she has very few options to stop Homelander and no emotional leverage except Ryan. So, this deal works more like a threat he can use to force her to comply with his demands.
Another reason Homelander might’ve kept Butcher alive is simply because he enjoys humiliating him. As showrunner Eric Kripke explained, Homelander’s weaknesses are physiological. His arrogance and vanity mean he could never consider Butcher to be anything more than an inconvenience, and certainly not a real threat. For now, he probably considers Butcher to be a useful tool to control Becca, but also he might enjoy the notion that he stole Butcher’s family from him. The pleasure he has knowing Billy is humiliated is greater than the pleasure he would feel by killing him.
Butcher had the right idea in The Boys season 1 by going after the supes’ emotional weaknesses, but he might want to rethink that strategy now that Homelander’s very short list of people he cares about includes Becca’s own son. For now, he’s determined to find Becca and help her escape the compound built by Vought International. Since Homelader took him there only for a brief moment, Butcher is trying to discover her location using visual clues he picked up, such as the types of trees in Becca’s yard. It remains to be seen if he will be able to find her by the end of The Boys. season 2.