In the film "Goodfellas", why was the character Tommy killed?

In Goodfellas, Tommy was killed because he killed a made Mafia member, Billy Batts.

Batts, played by Frank Vincent, had recently returned from prison and insulted Tommy DeVito at Henry Hill’s bar. Tommy, Jimmy Conway, and Henry beat Batts, stabbed him, and shot him. They then hid his body in the trunk of a car and buried it in upstate New York.

The killing was especially serious because Batts was presented as a made man in the Gambino crime family. Associates could not casually attack or kill a formally inducted member without risking retaliation. Tommy’s violent behavior also made him a liability, so the Mafia lured him to what he believed was his induction ceremony.

Instead of being made, Tommy was executed as revenge for Batts’s murder. The film’s explanation follows Henry Hill’s account, although the precise real-life status of William “Billy Batts” Bentvena has been debated by historians and Mafia researchers.