"Soul winning" is a phrase used one time in the Old Covenant scriptures (Proverbs 11:30) & it was never a term applied to New Covenant "conversion" or evangelism. New Testament evangelism wasn't focused on "winning" but on "proclaiming" the good news. It was never a burden to try to get people saved. It was a joy to tell people about Jesus & go from there. In the letters of the New Testament you don't see people being told to "get out there & win the lost."
The idea of "soul winning" often equals "winning" an argument or manipulating a stranger into saying a "sinner's prayer." If they do you invite them to church, hope they come, & never talk to them again. If you have to "win" people that means you "lose" if you fail to get them to pray a prayer.
So evangelism as pushed in most churches is a legalistic parroting that has nothing to do with the person you are talking to, it only has to do with you "making sure you witness enough" for God to not be disappointed with you. It is shame based & law based witnessing. Part of the gospel is that Jesus came to free us from both shame & the burden of the law. So if you talk to people about God because you have to & you'll feel guilty if you don't you're not exuding the results of the gospel at all. You're exuding the opposite.
I've seriously heard multiple people say that the MAIN difference between a Christian & a non-Christian is that God "convicts" Christians of their sins. Convict means "to charge with guilt, to make someone feel guilty, to shame someone by calling out their faults." According to this "the good news" is that if you become a Christian God will make you feel really really bad about everything you even slightly do wrong in your life.
Our conviction of sin guilt is imaginary. Scripture NEVER says that God convicts Christians of sin. It in fact says the opposite. God does not charge people with the guilt of sin (2 Corinthians 5:19). And God promises SEVEN times that He will never make us feel guilty or shameful (Isaiah 28:16, 45:17, 54:4, Romans 9:33, 10:11, 1 Peter 2:6, Joel 2:26-27).
So instead of freedom from slavery to sin, guilt, shame, & the law you are put into the maximum security prison of hyper law which leads you to believe that every single command in all of scripture was written for you to keep & every single moment of shame or guilt or obligation is God's "conviction." How foreign to the gospel this is! It saying being a Christian means there are more laws to keep & more shame being heaped & God charges you with sin more than ever.
No wonder people think they have to "win souls" because who would choose a God like that? People try to "win" souls like they try to win a war because their goal is to get people to "surrender" to God. Scripture DOES NOT USE the word "surrender" because God is not at war with us! He is our loving Father. He waits for His children to come home & celebrates with we who are already at home with Him.