The other fallacy is to apply reason and logic to faith.
Faith is a beautiful thing, and it exists completely outside reason. To try to "prove" faith through conventional methods is a fool's errand.
Actually faith and reason are not mutually exclusive. You are now guilty of the fallacy of false dilemma. Faith is a necessary component of everything we do, and we all have faith in one thing or another--including logic and reason itself (some of us do, anyway). Indeed, reason is a very important component of my faith. Without one, I could not have the other. Would you like me to elaborate?
I don't agree with the second half of the sentence.
Faith is not blind belief. True faith is putting your trust in something that has objective value. I have faith that my brakes will stop my car, having tested that belief millions of times over. I don't have faith that if I don't look down, I can keep walking off the edge of a cliff without falling like a Bugs Bunny character because objective reality doesn't work that way.
The Apostles had faith in Jesus, and they knew with 100% objective certainty whether or not the things they based their faith in--like whether or not He really walked around talking and eating with them after His execution. They were not faithless because they could prove their faith with an empty tomb, thousands of witnesses to Jesus' miracles, and the Old Testament prophecies.
Likewise, I believe in Jesus because I don't buy dozens of men deliberately lying about the obsurd proposition that a carpenter from Nazareth came back from the dead would go to their deaths for that lie without most or all recanting. I believe in Him because the Gospel accounts are historically reliable by every test we normally apply to such documents. I believe because Christianity prospered in Jerusalem, where it would have been the easiest thing in the world for the authorities to disprove had it been false. I believe because the Jews admitted that Jesus did miracles. I believe because Jesus Christ fulfilled hundreds of prophecies, because in Him the whole Bible (especially the strange and confusing parts) ties together, and because we see today exactly what the Bible predicted.
My belief is based on logical, historical arguments. My faith was the decision to, having come to that logical conclusion, put my life into His hands, and having done so, I can add my personal experience and growth to the reasons that I believe.
Faith in something worth having faith in does not require checking your brains at the door.