Essentially, they preferred the Muslims as their rulers.

The history of the Coptic Church under Islamic rule has quite a bit more nuance than that, and there are definitely many historians with for more knowledge on the subject that I, but from my own limited understanding of the topic Islamic rule was considered preferable to rule by other Christians.

The reasoning for this largely has to do with the persecution of the Copts by the Romans (both before and after the official adoption of Christianity as the state religion throughout the empire). Roman rule in Egypt was always rocky at best, so Christianity (which was rarely held in high esteem by the Palatium) being adopted by much of the Egyptian population only served to heighten tensions. These tensions typically spilled over into violence, such as Decius and Diocletians' persecutions. These tensions and periodic outbreaks of violence continued well into the Byzantine era, with the Orthodox emperors in Constantinople considering the Copts of Egypt to be heretics.

With the Muslim conquest of Egypt in 642AD, conditions actually became considerably better for the Copts. Mainly, this is because the Muslims, while by no means exceedingly tolerant towards the Copts, didn't really persecute them beyond enforcing the Jizya tax. There were some instances of violence, such as during the reign of Al-Hakim, a Fatimid Caliph, but it was never anything on par with what the Copts had seen during the reign of the Romans. This being coupled with a gradual adoption of the Arabic language in liturgical discourse led to the Copts being more or less subservient to Muslim rule, for the simple reason that, at least in Egypt, it wasn't all that bad.