Both Churches believe Christ is one Person Who is fully divine and fully human.
There is a lot of bad history that has yet to be resolved.
There are people who refuse to believe that "the other side" believes the same as they do, and who will go into schism if union is achieved.
There is the issue of councils. There are EO's who define the EO Church as a Church of 7 or 9 councils and they don't believe the OO's can be Orthodox without accepting 7 or 9 councils. The OO's, on the other hand, won't accept at least some of the EO's councils because of very bad history, etc.
There is the issue of what to do with saints who are condemned by "the other side." It's easy to say anathemas should just be lifted, but then some will say that is like admitting the Church Fathers were wrong in anathematizing them in the first place, and not everyone wants to admit their Church Fathers made a mistake.
There is the issue of differences in rites. The OO's have preserved a lot of the ancient local rites, and consequently have a lot of diversity in their practices. EO's are more uniform in practice, and at least a few will want the OO's to conform, which the OO's won't.
Whatever. I'm one of those who is hoping and praying for unity. A lot of things have to be ironed out though, before that happens. As Shanghaiski advised, however, I wouldn't get too caught up in the Chalcedon issues, as they get very contentious and unpleasant.