In the Midrash Rabbah we find two opinions on this matter:
Rabbi Yochanan taught that angels were created on the second day of Creation. He sees this reflected in Psalms 104 where we read in the third verse: "Who roofs His upper chambers with water," and in the following verse, "He makes His angels spirits…" He therefore concluded that the angels where created on the second day, the same day that G‑d divided the waters, creating an "upper chambers with water."
In addition, in the description of the story of creation (Genesis 1), there’s an interesting lingual anomaly. After the first day of creation the Torah says, "It was evening it was day, one day." After the succeeding days, "It was evening it was day, the second day... third day... fourth day... etc." Following this sequence, after the first day the Torah should logically have said, "It was evening it was day, the first day"? Why "one day"? From this our Sages infer that the first day was a day of "oneness," when G‑d was one and alone, for all His assistants, the angels, were created on the following day.
Rabbi Chanina, however, taught that angels were created on the fifth day. He points out that the words used in Genesis to describe the creation of the birds (on the fifth day) are similar to the words used by Isaiah to describe the angels (in Isaiah 6).
(Since all opinions expressed in the Torah are correct, as they are all "the words of the living G‑d," perhaps it can be said that certain groups of angels were created on the second day of creation, and others on the fifth.)
I hope that I've been helpful today.
Yours truly,
Rabbi Menachem Posner
The argument presented here is incorrect when applying the Law of logic. This statement violates the Law of excluded middle, as well as the Law of non-contradiction. Either one is true or the other is, but they both cannot be true and correct.
Your argument is certainly true when it comes to logical discussions, but Torah extends beyond logic and transcends rational thought processes. In Torah, contradictions most certainly can exist in harmony.