To talk about the language of Abraham is first to establish what historical period Abraham lived in. The Bible tells us that Abraham came from Ur of the Chaldeans, which is an anachronism, since the Chaldeans arrived in Mesopotamia around the 11th century b.e.v., well after the Exodus. Moreover, the word “Chaldeans” (kasdim in Hebrew) would derive from Chesed, one of Abraham's own grandsons, son of his brother Nacor. Let us therefore leave the Chaldeans aside.
Let us look at the chronology of the biblical account: in Genesis (15:13) it is written that the Hebrews would remain 400 years in Egypt; in Exodus (12:49) it is written that they remained there 430 years. Then, in the first Book of Kings (6:1) it is said that Solomon's Temple was built 480 years after the exodus, in the fourth year of Solomon's reign (about 968 b.e.v.). Calculating also the 40 years in the desert we have 400+40+480=920 years to add up to 968: thus 1888 b.e.v.; this is the date of Abraham's departure from Ur according to the biblical account.
During the period of the beginning of the 2nd millennium b.e.v., Old Babylonian, i.e., the southern version of Akkadian, the earliest Semitic language of which written records have come down to us, was spoken in lower Mesopotamia about a millennium before Abraham. In addition, Sumerian was still used as a sacred and ceremonial language.
The northern version of Akkadian is ancient Assyrian.
