Calvinists insist that Christ did not die for all men; rather He only died for the elect, but Paul is reminding the Corinthians of the gospel the he had preached to them which was that 'Christ died for our sins'.
Paul told non-believers that Christ died for our sins. We can only conclude that Christ died for all men without exception.
I hope this helps.
This is not at all how first person plural pronouns work. A first person plural pronoun is used to refer to any group of people including the speaker and any quantity of additional parties on whose behalf the speaker is speaking. That's it. Put in more technical terms, "our" can be inclusive: "you and I," or exclusive, "I and he/she/it/they."
If I have a wife and a house, and someone asks me what color our house is, and I say "our house is red," I haven't just given the listener ownership in our house. "our" meant "mine and my wife's," not "mine and yours." Whether or not "our" is inclusive of the audience is contextually determined, not grammatically determined.
Moreover, you can't even establish from this verse that Paul said the exact words "Christ died for our sins" to any unbelievers at any time. Paul wrote I Corinthians to the Church at Corinth. If context indicates that "our" is inclusive of the audience, the audience of I Corinthians are Corinthian Christians. These are the only people we can assume belong to an inclusive first person plural pronoun. Accordingly, lacking evidence that something is a direct quote, it can't be assumed that such a word was used when the audience was different.
Return to the house example. Say I've been asked if my house is for sale. I say "No, this house is not for sale." My wife asks me what I was talking about with the gentleman who asked about whether my house is for sale. I say "I told him our house is not for sale."
In this example, I gave my first statement to my primary audience - the man, and then I gave a statement about my statement to my secondary audience - my wife. When I used "our" to talk to my secondary audience, I was speaking inclusively of only my secondary audience. "Our" was not necessarily the pronoun I used in the primary statement - indeed, I didn't use a personal pronoun at all, but the demonstrative "this."
So had Paul said "Christ died for our sins" to people whose sins have not been forgiven via the vicarious atonement of Christ, there's no reason why this can't be taken the same way as had he said "Christ died for the sins of me and of the rest of the Church," exclusive of some in the audience; and it is not even clear that he said that, since we can only be sure the word "our" appeared in the text of Corinthians itself, and not in the earlier dialogues being reported in Corinthians.
