Papal primacy, purgatory, the immaculate conception, the filioque, among others are several doctrines that keep us separated.
I have tried to study Eastern Orthodox teaching, and these may seem simple, but they are huge impediments to union
In my studies, the EO do not accept the doctrine of original sin, so their argument is there was no need for an immaculate conception. I find that thinking very problematic.
As Catholics we profess that baptism washes away original sin as it bestows grace.
Mary is full of grace, so she was conceived without original sin. Genesis 3:15 prophesied that she would be the enemy of Satan. If she was a sinner, she would be a slave to sin and not its enemy. The EO agree that Mary was sinless, but not immaculate.
Then we have John the Baptist, whom Our Lord said there was no greater man ever born. There was Noah, Abraham, Moses, Elijah, Jacob. Our Lord puts John the Baptist above them, why?
Well if we accept the doctrine of original sin and baptism, we see that the other men were born in sin. John the Baptist was conceived in sin, yet received the sacrament of baptism while still in the womb, so he was born without original sin. Adam did not have original sin, but he was not born of a woman.
How do we know John the Baptist was baptized in the womb? Because he leaped for joy at the sound of Mary’s voice in the ears of his mother. When Adam sinned, he hid himself from God as he carried the shame of sin. John the Baptist leaped for joy. He was cleansed from original sin by the Holy Spirit who makes all baptisms effective.
That also is a teaching on infant baptism, but that is another matter. Simply put, if there is disagreement on original sin, that teaching makes no sense, and it makes it very unlikely that there would be unification of EO and Catholic without agreement on original sin.