In your personal opinion, what do you think the Shaddai in El Shaddai means? I know that there are different opinions on the meaning, so I was curious as to what your thoughts were on the subject.
Oooh, great question. I’m going to respond by asking: what do you mean by “means”? That is, are you looking for the original etymological origin of the term, or are you asking what it connoted to the biblical authors? The Bible is full of false etymologies, so those two questions do not necessarily have the same answer.
To the question of etymology, honestly, I don’t think that there’s an answer that is Clearly Correct. There are a number of options proposed, and I will tentatively follow the explanation in the Dictionary of Deities and Demons in the Bible (which is one of my favorite reference books, btw). (Sidebar: I was SO EXCITED when I found a copy in a used bookstore, given that Amazon now has it running for hundreds of dollars. Not that I would suggest you search for the widely available illicit PDF of it...)
Anyway! The DDD suggests that it connects to the Akkadian šadû (mountains) and the West Semitic sadeh (field/wilderness) to refer to the god(s) of the mountain wilderness. While it mostly appears in the singular in the Bible, it appears in the plural in the Deir Alla inscription, and I would guess that it originally referred to the “gods of the wild places.” It’s present in some of the Bible’s more archaic texts, as well as onomastic evidence, so it’s quite ancient.
The term was revived in popularity as a title of YHWH in later biblical texts like Job. (In fact, the Job usages may be due to its “exotic setting,” to indicate that its authors thought of Shaddai as an originally foreign term for God.) Early Greek translations of the term vary, but one common translation is “παντοκρατωρ,” “Almighty One,” so Second Temple era authors may have understood it as a term of power and omnipotence. This might be due to the false etymological connection to the verb ŠDD, which meant “to destroy violently.”
(Sadly, the proposed origin of “breasts” is probably incorrect, although it may be referenced in Genesis 49, which invokes blessings first from Shaddai and then from the breasts (shaddayim) and womb.)