Divisive Doctrines

My wife and I have been having an ongoing discussion about the divisiveness of words.
Her focus is on 1 Timothy 6:4, 20 and 2 Tim. 2:14, 23 which all talk about doctrines and words that cause arguments.
My focus is on 2 Timothy 2:25-26, which tells us to instruct those who are given to divisiveness.
This is not an issue of "Who is right? Who is wrong?" For, as can be seen from the verses quoted, both have their place.
We both have a problem in one of our Bible study groups with the bringing up of controversial doctrine.
I don't like it when the thought is not on point, but just seems to be someone's hobby horse. My wife doesn't like it because she can see where it will lead.
She wants it stopped before it begins.
I want the attitudes that engender the divisiveness to be stopped.
I feel we have an opportunity to show how we can learn to speak with gentleness rather than get heated because someone's view is different from our own.
She doesn't want the intensity to show up at all.

Discussion:
(please try to avoid a right/wrong in this)
What is your experience in these kinds of situations?
What do you feel is at the root of discussions that become heated?
What is the leader's responsibility when intense debate shows up in a gathering?

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