Faith in the most generic sense means "trusting in something outside yourself." That kind of faith is part of what makes humans different from animals--we can learn from others' mistakes instead of repeating them for ourselves. When we trust what others say, we can stand on the shoulders of their experience--dwarves on the shoulders of giants.
That's one kind of faith, but the New Testament uses the word in a more specific sense. The "faith" that Jesus talks about involves much more than merely trusting other people. Consider Mark 11:
As they passed by in the morning, they saw the fig tree withered away to its roots. And Peter remembered and said to him, “Rabbi, look! The fig tree that you cursed has withered.”
And Jesus answered them, “Have faith in God. Truly, I say to you, whoever says to this mountain, ‘Be taken up and thrown into the sea,’ and does not doubt in his heart, but believes that what he says will come to pass, it will be done for him. Therefore I tell you, whatever you ask in prayer, believe that you have received it, and it will be yours. And whenever you stand praying, forgive, if you have anything against anyone, so that your Father also who is in heaven may forgive you your trespasses.”
This kind of faith is hard to argue with. The Protestants who say they're saved by faith would impress their Catholic brethren more if they tossed a few mountains into the sea while they were at it. The secular materialist who scoffs at "faith" would scoff a little less if fig trees shriveled up around him.
The problem is, this kind of faith is rare, even though Jesus commands and demands it. The various branches of Christianity think they're going to Heaven because they believe the right doctrines, and the other branches are going to Hell because they believe the wrong ones. New Testament "faith" means more than merely mental assent to human propositions.
I'm not Catholic, but I'm not so sure that all the Protestants who confidently claim to be "saved by faith" are standing on solid ground. According to Christian theology, the redemption of a sinful soul is the greatest miracle imaginable. It only took God's word to make the heavens and the earth. It took the death of His own Son to save a sinner.
If your faith doesn't shrivel fig trees, what makes you think you're going to Heaven?