Being a superhero is all about self-sacrifice. Their job is to protect the innocent against the threats of evil supervillains. They rarely get thanks and they don't ask for any. Being a hero is a noble profession, even if most of them don't get paid to do the job.
In the Marvel Universe, the Avengers are the world's premiere team of heroes. They are labeled as Earth's Mightiest Heroes. Because of their deeds and the many times they have saved the world, they are looked up at and can even be considered role models for other younger heroes and even the public.
The number one rule for a superhero is 'heroes don't kill. As Avengers, this is a rule they should all live by. Once a hero crosses that line, it's not really easy to cross back over. There used to be an extremely rigorous application process. Now we're seeing known killers on the team. Should 'heroes' that kill without a second thought be allowed on the Avengers?== TEASER ==
The biggest example is Wolverine. This guy can have a temper that almost rivals Hulk's. When he goes into Berserker Barrage mode, anyone standing in the way better have a good life insurance policy for their loved ones. Wolverine will do whatever it takes to get the job done. He could be the ideal teammate to have watching your back in a battle. The fact that he will kill without a second thought is the problem.
There may be times when the odds are stacked against him. Sometimes the enemies can be so vile that he can't help but unleash his fury upon them. As an Avenger, that isn't the way they operate. Wolverine is a highly trained and skilled fighter. He should know a couple dozen ways to incapacitate a foe. Yet, when it gets down to it, he'll just start slashing away in the heat of the moment. He might control his killing ways while on Avengers missions but that doesn't change the fact that he is still a killer. As the leader of X-Force, there are no qualms about killing. This doesn't give the public a good impression.
It could be argued that Wolverine's time on X-Force is a secret. Very few know of the black ops team. Keeping it a secret doesn't make it okay. Wolverine has killed many and it doesn't matter how much they might have deserved it. That's not his decision to make. He should be held accountable for his actions and the Avengers could be seen as harboring a known killer.
Wolverine isn't the only killer on the team. There are other members that have killed for the government. Captain America's past as a soldier is not an issue here. But what about Black Widow? As a former spy, how many individuals has she killed during her missions or outside of missions as a spy?
There's also Red Hulk. Yes, he was an Army General but when he gained his powers, he stole advanced tech from S.H.I.E.L.D., hunted down Abomination and killed him. Beast is also responsible for killing several enemies during a Secret Avengers mission. This was the only way to save millions from a bomb set to go off but the Avengers didn't give it a second thought afterwards. What about Thor? Does it not count that he killed his brother, Loki, because they're gods and Loki was able to come back to life?
In this case, Mockingbird didn't technically kill Phantom Rider, she simply didn't do anything to save him. Yes, she was a hero and member of the West Coast Avengers but this was a guy that abducted and brainwashed her into having a physical relationship with him (which was obviously against her will). Hawkeye was firm that Avengers don't kill.
Being a superhero and fighting insanely powerful supervillains isn't an easy job. The odds are often stacked against them. Regardless, if they intend to be full-fledged heroes and public figures as part of the Avengers, killing should not be an option. They are not authorized to kill as far as I know. Part of their training should focus on incapacitating their enemies without killing. Captain America was a soldier but does not kill today. Other heroes like Spider-Man and Iron Man don't kill. Even at other comic universes you have heroes like Batman and Superman who refuse to kill as well.
Killing should not be an option. It isn't the place for the heroes to make that decision. Ironically it was Wolverine that mentioned once you become a killer you can never go back. It's one thing to kill in self-defense. But if the hero could have handled the fight differently, that's where it becomes a problem. Killers should not be seen as heroes. Because the Avengers are seen as heroes in the public's eye, they should not allow killers to run loose on their teams.