A revamp of Session Zero should resolve this
I don't want to pull the 'Stop talking about it or I'm kicking you out' since it is rarely done during the session time. It usually comes up after a gaming session.
You've got a bit of an expectations mismatch. What you need to do is to revisit Session Zero with everyone before the next play session starts. You believe that you have the support of all of the other players. This is a classic example of using the tool for handling small group dynamics to reach consensus. Voting is one such tool.
But before you use a small group vote1, if you think that the player will listen, you can try to get them to stop bringing this up away from the table by telling them directly, in private, roughly this (use your own words):
I really don't want to talk about this away from the table. What else do you want to talk about?
And if that doesn't work, then proceed with the vote.
You are the GM:
- GM: OK, let's get on the same page. I am not running a game where
Cthulu/Lady of Pain/Cain (or whomever) can be killed. Attempts to
kill them will always fail. No dice rolled, no skill combinations,
no cool moves. {This entity} is as permanent as Gravity is here on
earth. Do we have any questions on that?
- Players, 1 through X: Offer opinions/discussion.
- GM: OK, let's vote on this.
- Vote.
- If as you say, the other players are on your side, you then tally up
the votes.
GM: OK, the vote is 5 to 1 that this is the game we are playing.
Now let's play. I will not entertain any further discussion of this
topics, since it has been decided here and now.
If they ever bring it up again, you must remain firm.
"Sorry, we voted on this, no. That's a closed issue. What else do you want to talk about?"
And stick to your guns.
Your problem isn't whether or not this thing can be killed. The problem is that this player does not accept your ruling as a GM and is also not accepting the consensus of the other players at the table.
Your other problem? Your group's inability to establish a small group consensus.
For further tools used in building small group consensus, read here.
Caution
If the vote goes against you, the GM, then you need another session zero to figure out what game you all are playing. Work out an agreement with the other players. If you have the entire table wanting to kill the unkillable, and that isn't the game you want to run, don't run it. Ask someone else to GM.
Experience
Lots of experience in sticking to my guns after making a decision as GM and using voting to resolve disagreements in small groups (in game situations and out). And a few experiences where a GM stepped down when the group consensus went in a different direction. (Common observation by GMs in cases like this is something like: "I don't get paid enough for this aggravation.")
The conversation typically goes something like this:
"Neat idea, it doesn't work that way in this game world. No, this isn't negotiable. Another GM may like that, but not this one."
I've also seen loads of DMs and GMs do the same thing. Eventually, say No and back it up while getting the support of the other players. It's a thing that each GM now and again needs to do.
1 This was added to the answer thanks to a very helpful discussion with @guildsbounty. It is a little unclear how long and to what length "away from table" discussions have gone on, or tend to go on in this case, so the "give the benefit of the doubt" recommendation as a prelude to firmer measures may fit this situation. Only you, knowing all of the players personally, can gage that.
Has this approach (small group voting to establish a norm) worked for me?
This came up on meta, the question of whether or not using voting as a way to solve a social disagreement in a small group has ever worked for me.
Yes. I've been doing that since Boy Scouts.
Have we done that in a TTRPG?
Yes. In the vast majority of cases it clears the air and off we go.
There is of course the notable exception of our group (college age) putting to vote a difference of approach that killed the Traveller campaign dead on the spot. (In retrospect, maybe that group was already dysfunctional and we just didn't realize it).
As with any problem that is rooted in the social dynamics of a small group, it will depend heavily on the people involved. Per the caveat section above: you may learn some things about your group that you didn't know when you use this approach.