It is easier to believe that all humans are born free of sin than to believe in original sin of mankind. After all what is more innocent than a newborn. So in reality it is a matter of faith that we are all born into sin as opposed to choosing it.
The idea of the Immaculate Conception is that the Christ would not be born through woman that carried original sin. Since God decided to burden all mankind with original sin, he has every right to exempt whomever he desires from the stain of that original sin.
Also the idea is that the Pope is not infallible in all regards, only in the regards of speaking on maters of Faith and Morals. It is believed that it is not he the Pope or even the Church talking when the Pope speaks Ex Cathedra, it is the Holly Spirit speaking through the Pope. The Pope is called the Vicar of Christ because he is the “Earthly representative of God or Christ” . Yet, he is till only a man. Often a very human man with very real short comings and sometimes very many sins.
How do you know that Christ - who was wholly human and wholly divine - could not be born of a woman who carried original sin? Such a fact may not be “logical”, but logic has very little to do with the Divine.
If God can create the universe, can give life to the Earth, can part the Red Sea, can raise the dead, then He can overcome that small bit of “ill-logic.” He can “square that circle” quite easily.
Be very careful about how easily you accept human explanations about God’s decisions.
“It is believed” that when the Pope speaks Ex Cathedra, then he is infallible; but I do not believe it.
The Pope may be called the Vicar of Christ, but that does not make it so.
And I think Christ has many earthly representatives.
And then there is BLIND faith.
A belief that ignores logical proof or material evidence to the contrary.