Why did Villanelle kill that man?

Well, Villanelle so far seems to be portraying a fictional stereotype of a psychopath, showing little to no remorse and tends to look at most people as a means to end.

In terms of Anton, he is nothing more than a number to Villanelle. She even mentions that they will just keep sending "another one", showing how impersonal she finds him. Plus it may send a message about what she just previously experienced in prison...

However, in terms of her former handler, Konstantin, season one's narrative in some ways is about opening up a crack into whom Villanelle really is vs the beginnings of unraveling the world Villanelle thinks she lives in.

One of her past "fixations" is exposed to the audience, and Eve, but we don't really know if Villanelle would have followed through on permanently terminating that relationship or not, but further more, the early episodes have scenes where Villanelle is asked by her victims, 'Why is she doing this?' And Villanelle admits quite freely that she doesn't know, and then happily finishes her task.

But then Eve gives her information she has compiled on her that includes knowing that Villanelle works for some organization called, 'The 12'. Although Villanelle tries to blow it all off, I think perhaps the idea is that she is being used by an organization to no known end and that believing that Eve could gain an upper hand over her, begins to annoy her. .

But one reason that could really push Villanelle not to be compelled by Konstantin, is that he sent her back into the prison she once occupied in order to kill Nadia, but also set a trap to keep her locked up, because she had not been following orders by drawing too much attention to her kills. One she was suppose to make look like a suicide that clearly did not and her involvement with Eve continues to pull MI6 closer to The 12.

In addition she seems to want to disregard her own Russian heritage, as she becomes obsessed with Paris due to a past relationship, --and while in prison, she often prefers to speak English over Russian, ultimately meaning she [rightfully in this instance] isn't grateful for the prison experience/training and therefor is not grateful towards her handler either, since she knows he seems to be just be using her too.