Both of which fall into the "you've been given permission by the GM to kill these beings" category though. I'm not even disagreeing with the methodology (I use it myself as a GM specifically to make things easier morality-wise on the players). But I was responding to a proposed setting where the morality was decidedly more "grey" than that.
I also said that it depends on what the objective is. It's unlikely for a professional assassin to be in the cateogory of "I occasionally kill people because it's necessary for something else I'm trying to achieve", and far more likely they choose the profession because they like to kill people. At the very least, they find that earning money by killing people to be more in line with their base personality than say working at a local Inn, or being a guard, or investigator, or any of a number of other professions in which "kill for money" is not the entirety of the job. So... their algnment would be evil (unless, I suppose, they only ever use their assassin skills in the pursuit of taking out "stereotypical evil", maybe).
What about a postal worker who finds that the only way he can deliver mail to a particular address on his route requires that he kill somene or something that is blocking his path? That's the kind of scenario I'm talking about. He does not choose "kill people" as his profession. He's "delivereing the mail". He gets paid to do this. Perhaps he even views what he does as an important (dare I say it "sacred") service. But technically, killing that person/thing/whatever is being done solely so he can deiver the mail, which he's ultimately doing because he's being paid to do so. It's in his interest to deliver the mail. It's in the recipients interest to have their mail delivered. So that troll blocking the bridge on his route just has to go, right?
A good character might see if there's way to talk the troll out of blocking anyone trying to cross the bridge (or otherwise find a solution that works for everyone and prevents loss of life). A neutral character would see "this is in my way, I'm going to remove it in the most efficient manner possible. If that requires killing it, I'm not going to lose sleep over it". Again. I'm trying to point out that there is a range in there, which "killing in the pursuit of self interest" can be neutral, so only examining cases where that isn't true isn't terribly helpful.
Instead of leaping to "professsional assassin", why not see if you can think of any professions and situations where what I'm saying might actually be the case?
So Han Solo was evil then? I mean, he killed a boatload of people, and did it entirely for the reward money (at least that was his stated reason).
Setting aside his later characterization as disliking the Empire, if Solo had known that Skywalker was wanted and had been offered a reward for turning him in, would he have done it? And would that have made him evil? Or neutral? I'd argue he was neutral in either direction. If he'd decided to turn them in, that would be neutral. If he decided to take the job and fly them to Aderaan that would also be neutral. And if he kills some folks getting his passenders to Aderaan, he's still neutral. If he kills some folks capturing the fugitives and handing them over to the Imperials, he's also still neutral. That's what neutral is.
If he goes out of his way to kill people that's a different story though.
I get what you are saying here, but my issue is that you are basically engaged in a binary alignment paradigm. Someone must be good and engaged in not just good but "super good" in order to engage in any sort of violence/harm without the result being "evil". I'll note that you wrote the words "evil" a heck of a lot (and the word "good" a couple times), but not once does the word neutral enter the equation.
Where is neutral? What motivates a neutral character, and under what conditions is that character able to kill/harm without risk to his alignment that isn't the same conditions which would cause the same to someone with a good alignment? Because if you can't actually define a difference, then you are really just placing neutral under the same requirements as good.
You are correct that this is important for players and GM to discuss ahead of time (kinda for exactly the reason we're having this dicussion now. not everyone agrees on the terms). Me personally? I see neutral as an alignment that is less restricted from killing then good, but isn't as cavalier or careless about it (or even desirous of it) as evil. It's a range. In Champions, we'd distinguish this as good having a "code against killing", and evil having "loves to kill", with neutral having neither.
And yeah. Obviously this can varry wildly based on the theme and setting of the game itself.
It's even worse than that IMO. I've written this a couple of times already, and I'm still pretty baffled over how the PC group got to the point where they were in the other location, in the room with the pool in it, yet had apparently had zero actual conversation about what their plan was, or their reason for being there was, or what they intended to do once there.
IMO, that component is massively important to an alignment effect determination in this case. As I stated previously, if the entire party (including 4 paladins) discussed this and made the decision to go to that location (for whatever reason) and kill whatever was in the pool, then the CN character deciding to do just that was not at all out of keeping with the alignment of the character. If, however, the party discussed the suspect nature of the source of the information about the "creature in the pool" and had decided to go there and investigate what was there, and determine what it was and why these fiends wanted it killed (including proabable discussion of this maybe being something good that they could free and might help them against said fiends later), and then the CN character out of the blue just decided to kill it anyway, then that would fall heavily to the evil side of the alignment spectrum.
Context really really matters here.