In Léon: The Professional (1994) Léon kills Malky in Chinatown the same day Mathilda heads out to kill Stansfield.
It's implied that this killing was 'personal'.
Why did Léon want to kill Malky then?
It's implied that this killing was 'personal'. Why did Léon want to kill Malky then?
Because it had become personal to him almost as much as to Mathilda.
Mathilda had won the Russian roulette game proving that she loved him (there was a bullet in the chamber but Leon saved her life by forcibly directing the revolver away of her head when she pulled the trigger).
Leon couldn't help appreciating that and so he made himself involved in her personal vendetta (although he didn't tell her) — after previously refusing to kill the scumbags even for $20k she had offered.
Before leaving to kill Malky, he said to her that she couldn't accompany him this time because the job was "too big" and that he needed some time alone to "grow up".
So, he just started doing what Mathilda would have clearly attempted to do anyway — to save her from the need to risk her life. He started with Malky apparently because he was away from the rest of the gang and so, easy to clean.