2 Corinthians 3:14-18
Seeing then that we have such hope, we use great plainness of speech: And not as Moses, which put a vail over his face, that the children of Israel could not stedfastly look to the end of that which is abolished: But their minds were blinded: for until this day remaineth the same vail untaken away in the reading of the old testament; which vail is done away in Christ. But even unto this day, when Moses is read, the vail is upon their heart. Nevertheless when it shall turn to the Lord, the vail shall be taken away. Now the Lord is that Spirit: and where the Spirit of the Lord is, there is liberty. But we all, with open face beholding as in a glass the glory of the Lord, are changed into the same image from glory to glory, even as by the Spirit of the Lord.
The vail remains upon their hearts as long as the are carnal, and being carnal, they are limited to seeing only things that pertain to the flesh. While they are yet carnal, they remain blinded to the old testament, even unto this very day. But that vail is done away with when we turn to the Spirit.
Now some might say that they can see the prophecies in the old testament as they relate to the virgin birth and the coming of the Jesus the Messiah, but these prophecies were the fulfillment of a carnal manifestation of the Son of God. But it is not the carnal manifestation that remains hidden when reading the old testament. What remains hidden behind the vail is the works and manifestation of the Spirit.
The carnal mind seeks to worship the image of a man as a God, and as long as they seek after the image of a man, will the remain blinded to the Spirit?
Romans 1:21-23
Because that, when they knew God, they glorified him not as God, neither were thankful; but became vain in their imaginations, and their foolish heart was darkened. Professing themselves to be wise, they became fools, And changed the glory of the uncorruptible God into an image made like to corruptible man, and to birds, and fourfooted beasts, and creeping things.
How shall we be changed into the same image from glory to glory, if that image is made like to corruptible man?
Hebrews 10:20
Having therefore, brethren, boldness to enter into the holiest by the blood of Jesus, By a new and living way, which he hath consecrated for us, through the veil, that is to say, his flesh.
Their minds were blinded unto this day when reading the old testament, because the veil of his flesh still calls to the carnal mind.