It's a sales technique. I am in sales, and when I'm trying to get a new customer signed up, I generally avoid the word "contract" like the plague. The document I'm trying to get them to sign is a "service agreement", or even just a "service order". No one wants to sign a "contract"; if you do that, youre "locked in". But entering into an "agreement" is a lot more acceptable in most people's eyes. It's the same thing, just different wording that makes a big difference in the eye of the beholder.
I think that they avoid the word "convert" simply because that's the word most people associate with changing religions, and, of course, they don't want to admit up front that that's what they are trying to get you to do. All of us as former JW's know that what we want to do right from the git-go, when we knock at a door, is ultimately to get the householder to change his or her religion, but most JW's, if asked directly, "Are you trying to convert me?" would answer no, we're just trying to "encourage Bible education". If pressed, they might admit that, given enough of their "Bible education," (which has little to do with the Bible), the householder will see no option other than becoming a JW, but they will insist that that is the householder's decision, that they are there only to present the Bible's message.
I once knew a CO who was refreshingly honest in this area. If someone asked him, "Are you trying to convert me?", he would answer, "Why, yes. I am!" and proceed from there in his presentation. I think it was Anthony Conte, but I'm not 100% sure it was him; it may have been another CO.
Of course, biblically, "conversion" refers to the turning around involved in repentance and changing one's life over from a worldly to a Christian way of living, and not merely to a change in organizational membership; but popular usage has somewhat corrupted from that original meaning.
Tom
"The truth was obscure, too profound and too pure; to live it you had to explode." ---Bob Dylan