One Day, Sir, you will actually address the biblical view.
1 Corinthians 9:22 (NASB)
to the weak I became as weak, that
I might gain [win] the weak. I have become all things to all
men, that I might
by all means save some.
Does this verse indicate Paul, rather than God actually saves individuals? Nope The idea is through evangelism, humans aid in bringing people to an understanding of the gospel, acting as ambassadors of Christ. How might we "win" or persuade or contribute to the understanding of lost individuals? Do we talk people into Christ? Nope. God alone puts individuals whose faith He alone credits as righteousness into Christ. But we can till the ground, helping to prepare an individual to receive the gospel, and we can plant, presenting God's word concerning the gospel, and we can reinforce a lost person's consideration of the gospel by fellowship and example.
At the heart of the issue is not anyone claiming to save people, a false claim used to deflect, but whether or not lost people can be receptive to our witness, which of course Calvinism denies, i.e. the "T" of the TULIP.