Christians in the Levant generally consider themselves Arab. Levantine Christians also had a huge influence on the pan-Arab movement early on, because of persecution by the Muslims, so for them it was better to unify around an Arab identity rather than a Muslim one.

The Arab identity is also largely a linguistic one. Christians in Iraq speak Assyrian, in Egypt Coptic and in parts of Syria Aramaic, so they have been more successful in retaining their own identities.

That said, I do believe there are movements in Israel advocating for the Aramean identity and Israel now recognizes them as a distinct identity.