"Division does not immediately come from disagreement but rather from those who take action upon it." - Kevin Johnson
I've heard countless times from church leaders that to disagree with the pastor/church/doctrinal statement, etc., means one is "divisive." Holding to beliefs other than the official beliefs of the church is viewed as very problematic, no matter how much a hero Martin Luther is to them in holding to beliefs other than the official beliefs of the Roman Catholic church - an act and an attitude that started the Protestant Reformation - to which they heartily agree.
As you can gather from the above quote, division is caused by people taking action on disagreement. Divisiveness is the state of causing division. If I disagree with my church about something, but I resign myself to attending there in spite of my difference, I am not causing division. I am helping the body remain intact as one. On the other hand, if I disagree with my church about something, and they ask me to leave, the church is the one that is causing division. They are dividing me from them.
Of course, there may be a good reason for the church to divide from an individual - such as a failure of church discipline to bring about repentance for a sin committed. But simple disagreement over a doctrinal issue doesn't necessarily imply that disagreement is sinful. So, to divide over such a thing, and to be somebody who has a habit of dividing over such things, is what division and divisiveness are.
In addition, to "cause division," as many like to put it, I would have to recruit somebody to my cause and sway them to divide from others. This is what it means to cause division. Merely disagreeing with church leaders is not in and of itself the causing of division. Realizing that there may be others who disagree also and hold to the same view as you and having lengthy discussions with those people is not causing division, either.
So, whenever I hear references to causing division or to divisiveness, I try to make sure just who it is who is doing such things, if they are doing those things at all.