I'm not sure what the objection here really is. Maybe someone could explain to me why anyone would object to someone making their points with Scripture.
1. If someone is correcting me in error, I am not going to be convinced by their good arguments sans Scripture. I need the Bible. I need chapter and verse. If I'm off-base, tell me where, chapter and verse!
2. If someone is wrong in their teaching, I need to know where they are getting it from. I need to know, chapter and verse, what they are basing their understanding on. If I think they are wrong, I need to know how they came to their conclusion and what verses that may be misapplying. How can I do that without them quoting Scripture?
Yes, the word is divisive. That's one of it's God-ordained functions.
Hebrews 4:12 For the word of God is quick, and powerful, and sharper than any twoedged sword, piercing even to the dividing asunder of soul and spirit, and of the joints and marrow, and is a discerner of the thoughts and intents of the heart.
Now if this complaint is that some people lack grace, what does that have to do with "the Sword?" "Sword wars" seems to be something negative the way it's been used here, but it's something God has commanded us to do. The word of God is a sword, and it is our offensive weaponry. It is what we are to use to correct error and preach. It hardly seems like a problem that there is too much usage of Scripture. If anything, there isn't enough.