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What was the reasoning?
There are many reasons given by the Church Fathers. Some of them are:
The great Franciscan theologian, Duns Scotus, explained ca. 600 years ago that falling into sin could be likened to a man approaching unaware a massive 20-feet deep ditch. If he falls into the ditch, he would need someone to lower a rope and save him. But if someone were to warn him of the danger ahead resulting in the man not falling into the ditch at all, he would have been saved from falling in the first place. Analogously, Mary was saved from sin by receiving the grace to be preserved from it. But she was still saved.
She is seen as a type of the Ark of the Covenant. Like the Ark which was protected from impure touch (2 Samuel 6:7), Mary is considered to be protected from Original Sin. (There are other similarities between Mary and the Ark too)
She is called Full of Grace by God the Father. Here the word grace (kecharitōmenē) is perfect passive participle. This word — kecharitōmenē, means not only full of grace, but the grace was bestowed in the past to the fullest extant possible and is ongoing. This is interpreted to mean she is sinless. Because Grace cannot be full if there is sin.
And do Protestants universally reject this?
It depends on what you mean by Protestants. But most protestants do not accept it. But some protestants like Anglo-Lutherans do.
Was she the only human to have been born this way besides Adam and Jesus?
Officially (at-least according to Catholics) we know for sure that Jesus and Mary were born sinless (Adam was created sinless). But some believe St. John the baptist, even though conceived in original sin, was purified in womb during visitation, making him technically sinless when born. Some also include St. Joseph in this list. But these are not official dogmas and one may choose not to believe in them.