Bible Quote: "All Men Have Not Faith"

But doesn't the Bible tell us again and again to believe? Why then would not our belief save us?

Yes, we are commanded to believe on Christ. But the belief is not to come from our physical minds. It is to come from the heart. And the heart is synonymous with the soul. We are commanded to believe in our souls (hearts):

Romans 10:9 That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.

10 For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation.

Believe from your heart (soul) and then confess with your mouth. But this is something impossible for man to do. Man cannot believe from his soul because his soul is dead in trespasses and sins. This is why the Bible tells us that all men have "not faith":

2 Thessalonians 3:2 And that we may be delivered from unreasonable and wicked men: for all men have not faith.

So, free will preachers, doing their best to stir up the congregation to exercise their belief in Christ, are preaching to those who are spiritually dead and utterly incapable of mustering up any faith whatsoever from the location of their soul. Man in his sin lacks faith. He doesn't have it. He doesn't possess it. It's not in him. He's dead in soul. Which is why such preaching is vain and empty and always a failure to accomplish its stated purpose of salvation for the sinner.