What language did Abraham, father of Ishmael and Isaac, speak? Was it related more to Arabic or to Hebrew, or both or neither?

What a turn up. After scouring Google I could place a 50/50 bet on both colours and still not win. Half the sites say Aramaic, the other Hebrew, and another half (if that's possible) say Babylonian! Here is a little excerpt of one site anyway:

Whether Abraham already spoke the language of Chanaan at the time of his migration, or whether, having first spoken Assyrian or Aramaic, he later adopted the language of the country in which he established himself, it is hard to say. But be that as it may, the language spoken by the clan of Abraham was a dialect closely akin to those of Moab, Tyre, and Sidon, and it bore a greater resemblance to Assyrian and Arabic than to Aramaic.

https://www.catholic.com/encyclopedia/hebrew-language-and-literature

Abraham identifies himself as an "ívri" - which means a descendant of Ever and a speaker of "ivrit" or Hebrew. The Hebrew language is related to other Semitic languages, among them Assyrian, Canaanite and Aramaic. Aramaic really had its high point around 2,000 years ago (long after Abraham), and Arabic really started to develop later (certainly what we know as modern Arabic did not exist 2,000 years ago).

People who travel generally learn a wide range of languages. And Abraham was one of the most traveled people of his day. He would have probably been fluent in Assyrian and Chaldee (the language of the countries in which he lived), and would have picked up quite a bit of Canaanite on the way. He may have spoken Egyptian. All these, mixed together, were really what made up the Hebrew language. Much as English is a mix of Latinate and Germanic roots, Hebrew is a mix of Assyrian, Canaanite and (to a lesser extent) Egyptian.

"Ur of the chaldees" is a misnomer for the Ur of Abraham's time, as many Bible critics have pointed out. "Chaldean" was associated with Alexander the Great, so that does not fit. Aramaic does not fit either for Abraham. Aramaic came later in about the 12th century BC, and was spoken in Jesus' time and afterwards.

So that leaves Sumerian, Babylonian, and Assyrian as possibilities (among those mentioned anyway) for the language spoken in Ur. What's Assyrian anyway? Wasn't the language of Assyria called Akkadian? The same with "Babylonian." That was Akkadian - the language of Babylon and Nineveh. Frankly, if I may say so, it looks like a lot of people don't know what they're talking about.
Akkadian was influenced by Sumerian early on. According to Wikipedia, the Akkadian dialect spoken in Abraham's time frame would have been Old Babylonian/Old Assyrian, with "Old Babylonian" being the same as "Sumerian." So it's a Sumerian/Old Assyrian mix, but the language is actually called Akkadian, and that is what would have been spoken in Ur. It's not as if archaeologists don't know the answers to these questions.

I'm not even going to start on what kind of Canaanite language Abraham and his descendants might have picked up. That is enough research for now. I will only say Hebrew came along later, and is definitamundo not the language that Abraham would have spoken in Ur.

Much depends on Abraham's birth place, which since Wooley's digs, most have placed in the Sumerian Ur. But CH Gordon posited a half century ago a different Ur located north of Haran, where possibly Amorite was spoken. Abraham's grand nephew Laban, whose father stayed behind in Haran, is depicted in Genesis as giving an altar an Aramaic name when Jacob gives it a Hebrew name, suggesting that Aramaic would have been Abraham's native tongue as well, but when we say "Aramaic" we are speaking of a language unattested epgraphically before the 9th century BC, many centuries after Abraham's time.
If it were true that Abraham were native to Sumer he would have spoken Akkadian, but it is quite unlikely that "Ur of the Chaldees" refered to the Sumerian Ur made famous by Wooley. So about the best we can do is suggest that maybe Abraham spoke "Proto-Aramaic" or Amorite. Hebrew was the language of Canaan of the first millenium BC, wherein Abraham was a stranger a thousand years earlier, and the passage in Jubilees attempts to account for the incongruity than in Genesis Abraham appears as a Hebrew speaker, an idea taken for granted by the compilers of Genesis with no linguistic self conciousness whatever.
--AGF