It does sound weird.. Although I think technically it's ok since in Arabic we refer to it as "The Celebration," since the word "Eid" literally translates to celebration or festivity.
It's kind of weird to call this one "The Eid" coz the two major celebrations are both "Eid" this is "Eid Al Fitr" (Celebration of the Feast) which celebrates the end of the holy month of Ramadan, it's a 3-day celebration. The second one (which is the big one) is "Eid Al Adha" (Celebration of the Sacrifice) is a 5-day celebration which comemorates Abraham's willingness to sacrifice his first-born son, Ismail. This celebration also includes "The Day of Arafa" which is the day that Islam, as a religion, was complete with the final verse of the Qur'an.
