Sometimes Anthony explicitly kills things. The episode begins with Anthony explicitly telling the three-headed gopher he'd created and was playing with to "be dead".

ANTHONY: I'll make him dead now. I'm tired of playing with him. Be dead. Gopher, you be dead!

MAN: It's real fine that you done that.

Later, an angry man accuses Anthony "You murderer!" Anthony changes an angry man into a grotesque human jack-in-the box, his father kneels down next to Anthony and says (with perhaps seeming compassion?)

FATHER: Wish it into the cornfield. Please son, wish it into the cornfield. Please!

ANTHONY: He was a bad man.

We can't be sure if Anthony's father simply wanted the grotesque creation out of sight, or if he felt this would terminate whatever level of life or awareness the jack-in-the-box/human conglomeration maintained.

There may be some further clues from the original story.

According to YouTube Channel Fever Dreamland Theater's It’s A Good Life - Twilight Zone Episode REVIEW the story first appeared in "STAR Science Fiction Stories Number 2" edited by Frank Pohl as Jerome Bixby's short story of the same name, so there may be clues.

I'll try to get a copy tomorrow, but if someone has one handy please feel free to edit here or write a new answer based on the short story.

Sometimes Anthony explicitly kills things. The episode begins with Anthony explicitly telling the three-headed gopher he'd created and was playing with to "be dead".

ANTHONY: I'll make him dead now. I'm tired of playing with him. Be dead. Gopher, you be dead!

MAN: It's real fine that you done that.

Later, an angry man accuses Anthony "You murderer!" Anthony changes an angry man into a grotesque human jack-in-the box, his father kneels down next to Anthony and says (with perhaps seeming compassion?)

FATHER: Wish it into the cornfield. Please son, wish it into the cornfield. Please!

ANTHONY: He was a bad man.

We can't be sure if Anthony's father simply wanted the grotesque creation out of sight, or if he felt this would terminate whatever level of life or awareness the jack-in-the-box/human conglomeration maintained.

See also @FuzzyBoots' answer

There may be some further clues from the original story.

I'll try to get a copy tomorrow, but if someone has one handy please feel free to edit here or write a new answer based on the short story.