Except that in the Bible it does not have that meaning.
HEBREW
דָּבַק dāḇaq = KJV Translation Count — Total: 54x
The KJV translates Strong's H1692 in the following manner: cleave (32x),
follow hard (5x),
overtake (3x),
stick (3x),
keep fast (2x),
...together (2x),
abide (1x),
close (1x),
joined (1x),
pursued (1x),
take (1x).
GREEK
προσκολλάω
proskollaō =
KJV Translation Count — Total: 4x
The KJV translates Strong's G4347 in the following manner: cleave (2x),
be joined (1x),
join (one's) self (1x).
So in the KJV, it is the EXACT OPPOSITE of what you are positing. Be careful my friend and go by what is actually in Scripture.
Well, you just proved my case. You provided dictionaries for a particular word that gives multiple meanings or definitions. So the word “cleave” can have several meanings or definitions just like other words and not just one. Just because the Bible uses the word “cleave” in a particular way does not mean it does not have other meanings. The origin of the word “divide“ means separate into parts or pieces (14th century). The King James Bible came out in the 17th century (1600s). The word “divide” in the intransitive sense of "become separated into parts" is from the 1520s. This is not too far off from 1611.
If we were to look at the time the KJV was translated, it has a meaning to divide like in the execution of a rapid melodic passage, originally conceived as the dividing of each of a succession of long notes into several short ones.
https://www.oed.com/dictionary/divide_v?tab=meaning_and_use#6309369
But again, the idea here is dividing (Separating two things).
We read in the story of Solomon about how he was to DIVIDE a baby to resolve the TRUTH of the matter (1 Kings 3:16-28).
The word of God is like a two-edged sword that DIVIDES soul and spirit (Hebrews 4:12).
The Old and New Testaments are divided in our Bible.
We must rightly divide between the Old Covenant and the New Covenant.
We must rightly divide between God’s grace and Sanctification.
We must rightly divide between the milk of the Word vs. the meat of the Word.
God wants us to divide.
Jesus (GOD) said,
”Suppose ye that I am come to give peace on earth? I tell you, Nay; but rather division: For from henceforth there shall be five in one house divided, three against two, and two against three. The father shall be divided against the son, and the son against the father; the mother against the daughter, and the daughter against the mother; the mother in law against her daughter in law, and the daughter in law against her mother in law.” (Luke 12:51-53).
God divided the light from the darkness even at the beginning (Genesis 1:4).
So you cannot say that "dividing" in 2 Timothy 2:15 does not mean divide as we understand that word.
The Bible certainly does use it to mean to cut, separate, or distinguish between two things.
Solomon said, divide the living child in two (1 Kings 3:25).
This was to cut him in two pieces. Granted, he did not intend to hurt the little one, but it was to reveal the true mother.
But the point here is divide can mean "cut in two" according to the Bible.
When I look at the whole counsel of God’s Word on dividing (cutting or separating) between various truths in the Bible, that makes a whole lot of sense with 2 Timothy 2:15.
So I am using examples in the Bible, and I am not just pointing to a dictionary alone, my friend.