If man comes to Christ through only free will, and not through the sovereign election of God, then that means when you (if you are a Christian) witness to someone, if they do not accept Christ, it is at least partially your fault, because if you had done a better job presenting the gospel, they might have come to Christ. So therefore, their eternal damnation could be in part because you did not do a good job evangelizing. So therefore, from that perspective, we are partially responsible for someone's salvation or damnation. If the lost person is free to choose or reject the gospel, and if it is completely up to them alone, then if the Christian who is witnessing to them doesn't present the gospel in a way that persuades that lost person to want to accept it, then that Christian presenting the gospel is at least partially at fault, because if they had done a better job, that lost person might have been saved. When a Christian witnesses to people and presents the gospel to them, and people do not respond – if that Christian really thought that it really depended on them (the fact that the lost person didn’t respond), it is feasible that the Christian could possibly even become extremely depressed and, in guilt and anguish...well, I could even imagine an extreme instance where a Christian who believed that, might even go home and pull out a knife and plunge it into their heart because they were such a failure, and because that lost person, or those lost people, going to Hell would be partially their fault, because their gospel presentation was not compelling enough.
On the other hand, if salvation is up to God's sovereign election, then when we witness to someone, all we are responsible for is to tell them, and we don't have to worry about the outcome, because that is up to God.
Ultimately, the salvation of souls depends upon the Lord God, and he has graciously given us the opportunity of being instruments in the accomplishment of his work. We (if we are born again, regenerated Christians whose lives have been radically transformed by the power of the Holy Spirit) are called to partner with Him and share in the great and glorious work of the Great Commission. We get the easy part (telling), and He does the rest. No higher calling could any individual ever have than being a co-worker with the Lord.