The Coptic church has been out of communion with Rome and Constantinople since 451, and the reason is a single technical formula about how the divine and the human are joined in Christ.
What happened at Chalcedon
The council defined Christ as one person in two natures, divine and human, without confusion or division. The Alexandrian tradition, following Cyril, had spoken of one incarnate nature of God the Word, and read the two-nature formula as dividing Christ in half. Dioscorus of Alexandria was deposed at the council, and the churches of Egypt, Syria, Armenia and Ethiopia went their own way.
Why the old label is wrong
For fifteen centuries these churches were called monophysite, meaning one nature, with the implication that the humanity was absorbed into the divinity. That is the position of Eutyches, and the Coptic church condemned Eutyches too. The term now used, miaphysite, marks the difference: one united nature in which the divine and the human are each complete and neither is diminished. The distinction is not pedantry, because the charge being answered is that Christ was not fully human.
The agreements nobody expected
Since 1971 a series of joint declarations between Coptic, Catholic and Eastern Orthodox theologians have stated that the two formulas express the same faith in different vocabularies, and that the condemnations of 451 were aimed at positions neither side actually holds. Communion has not followed. Doctrinal agreement and ecclesial union are separate problems, and the second involves questions of authority the first does not touch.