How can we be convinced about things that cannot be seen (He.11:1)? Only when we believe they are true. When something is true, the opposite cannot be true also! If something is white, it cannot be black at the same time, even if someone believes it is black. So, our faith must be based on facts. When we say 'facts' we mean they are true. If they are imaginary, we can't call them facts.
Some people try to be very philosophical and say that whatever anyone believes is 'real' for them and others should not interfere with their faith! But if someone believes something is black when it is actually white, he is mistaken! If what he believes is wrong, his so-called faith is not going to do him any good, is it? On the contrary, it will mislead him and he will miss out on the truth that can save him (Jn.8:32). Doesn't it become the duty of those who know the truth to help those who are mistaken so that they too can find the truth?
Another aspect of Christian faith is that faith is not something that describes a state of our mind or a set of beliefs but a trust and confidence in God that causes us to yield our lives to Him and live according to His ways. Those who think it is a state of mind assume they have to somehow make themselves believe certain things and that when that happens, their faith is going to cause things to happen. Those who describe faith as a set of beliefs in their mind imagine that if their beliefs are right, automatically good things will happen to them. Both these groups of people assume that it is their 'faith' that will cause things to happen. But the truth is that it is God who alone can make things happen for us, when we place our trust in Him and not in ourselves.
Even though it may look as if we are trying to split hairs here, actually their implications are very practical! Only the right type of faith will work! If we have the wrong type of faith, we may keep hoping that it will work, but when our life is all over, we will discover that we lost our entire opportunity to know the truth.
There were two occasions when Jesus praised someone's faith, that of a Roman centurion (Mt.8:5-10) and a Gentile woman (Mt.15:22-28) whose daughter needed deliverance. Two common things from both cases are: they had complete confidence in Jesus as a Person with His ability and goodness of heart to do miracles for them, and they were both convinced about their own smallness. So instead of leaning on their own power or their faith they leaned on Jesus. Those were two sides to their conviction: they knew they could not handle their situation and that Jesus could. That is true faith.
A very common mistake nowadays is that people place confidence in their faith (indirectly on themselves) instead of leaning entirely on God. Many don't even give God an option to make any decision on their behalf! They think that if they have enough faith, God is bound up by that faith to give what they want. No. Submit to God!