Why did the Coptic Orthodox church break away from the other Orthodox churches?

Not only the Coptic, but also the Armenian, Syrian, Ethiopian and a few others form a group called the Oriental Orthodox Churches.

They did not accept the Council of Chalcedon in AD 451 since it declared Christ to be "in two natures" (human and divine), rather than "from two natures".

The difference is merely semantical (although some Eastern Orthodox would disagree), a misunderstanding at the time, fuelled by political issues.

Efforts to unite the two strands of Orthodoxy are underway, but unlikely to succeed, given this may split the Eastern Orthodox (eg Greek, Russian) communion in two.