When we are witnessing to someone and the person responds positively to the gospel, it is natural for us to want to declare them saved. But is that what we should be doing?
Here are some reasons not to:
How do we know they are genuine?
Even if the person you are witnessing to says he is now believing, there is no way to know if he is sincere. He could simply be making a profession of faith because he knows it will please you, or because of peer pressure, or because he knows it's what he should do.
Easily creates false converts
We should tell people how to be saved, but it's not our job to declare them as saved. Otherwise, we'll easily create false converts - those who think they are saved but don't truly trust in Christ for their salvation and hence probably live like the devil. It is far worse for a person to be a professing Christian and not really be one, compared to someone who knows he is not a Christian and doesn't say he is one (2 Pet. 2:21).
A person's assurance shouldn't come from your declaration
Many people think they are saved because a Christian at one time said to them, "You are saved". Maybe it was after they walked an aisle, signed a card, or prayed a prayer. The issue is that their assurance is based on performing a work rather than the fact that the only thing they are presently trusting in to save them is Christ's death and resurrection. And Scripture is clear in saying works don't save (Eph. 2:8-9).
A Christian can have complete assurance of salvation if he is trusting in what Jesus has done to save him and his lifestyle change will further attest to that. But we don't need to declare someone saved, our job is to be faithful in declaring the news of what Jesus has done to save sinners and how through faith we can receive that gift of forgiveness. A person will know he is saved if he is genuine, you won't have to tell him.
So what should we do instead if someone responds positively to the gospel?
Check that the person has understood the gospel. Ask something like, "So if God asked you, 'Why should I let you into heaven?' What would you say?"
Encourage him to count the cost of trusting in Christ, but at the same time not to delay.
Point him to a local Bible believing church and encourage him to read the Bible daily.