False Belief

There are several options concerning confusion and assurance in salvation.

╖ Saved and believes they are not saved
╖ Saved and believes they are saved
╖ Not saved and believes they are not saved
╖ Not saved and believes they are saved

So, from the logical options, it is possible for someone to believe that he/she is saved, but to be mistaken in this regard. In fact, the Scriptures give us some good examples of this (e.g. John 5:39-40; 8:39-45), and Jesus himself taught this in the Sermon on the Mount (Matt. 7:21-23). Paul also indicated this (e.g. 2 Cor. 13:5).
How then can we have assurance of our salvation? Well, the Bible provides the answers. For example, many passages (e.g. John 15:8; Phil. 2:12-16; Heb. 6:11; Jam. 1:22; 2 Peter 1:5-10; 1 John 2:3-6; 3:7,10,18-19) suggest that by pursuing righteousness in our lives we may assure ourselves of our salvation. This is not, of course, and ironclad proof. It is very subjective, but then so is the feeling of assurance; we may also be saved and yet not be assured of it.

Another way to be assured of salvation is to compare the gospel we believe to the Bible's idea of the gospel. If we believe something other than what the Bible teaches, we are certainly not saved (Gal. 1:6-10). But if we believe what it teaches, if we have the faith of which it speaks, then we are saved (e.g. Rom. 3:21-22; 10:9; Col. 2:2; Heb. 10:19-22).

Another way to gain assurance is to pray for it. God does not desire that his children doubt their salvation. Rather, he desires that we have peace and comfort in him (Phil. 4:6-7). By his Spirit he will grant us comfort and assurance.
One way to languish in doubt is to concentrate solely on the sin in our lives and fall into despair (e.g. 1 John 3:18-20). The fact that we continue to need Christ's forgiveness is not proof that we are not saved (e.g. 1 John 1:5-2:2). And the fact that we struggle with sin is an indication that we are saved: those who are not saved are not grieved by the fact that they don't please God -- they don't want to please him (Rom. 8:7).

As I stated initially, assurance of salvation may be false. But the Bible provides "tests" for us by which we can try to figure out if our assurance is false (1 John has many of these tests). But assurance may also be true and God-given. Because it is possible for us to be wrong, we cannot "prove" that we are saved in a way that will be completely compelling in all circumstances and to all people. Nevertheless, we can be personally and individually assured of our salvation in such ways as I have mentioned (and in others, too). Our assurance ought not to rely on absolute, verifiable, unquestionable "proofs," but on the Holy Spirit who comforts us and assures us when we evaluate ourselves by the Bible's standards that we are indeed secure in Jesus.