I think initially people would like to be proved wrong, that people sincerely care. But they find that except for the canned "encouragement" all real, caring contact drops off and disappears.
That's what it is. Speaking for myself, I felt that many JW's in the congregation were genuinely concerned about the supposed life-saving work. I believed that they believed Matt. 18: 12,13 about wanting to go help the single lost sheep.
So wanting them to "come after" me was like a last stand. I felt that, sure the doctrine was wrong, but the love and concern of the individuals could override that problem. It turns out that it cannot. Deep down, as a previous elder, I knew that they only could offer cold insistence that I believe the doctrine and do the bidding of the WTS Governing Body or else. I knew that their only message close to "love and concern" was that they would fully welcome me back into the fold if I went to most meetings and stayed "regular" in field recruiting.
So, leaving was an exercise in proving to myself that it was more than just "not the truth" but was actually a "dangerous mind-control cult."
If you want to look at it a lighter way, suppose you know that a former very close friend is getting married. You've lost some contact with that former friend because your lives have gone down different paths. You may not want to go to the wedding, but you still feel a bit forgotten or insulted when they do not send you an invitation. You were going to send a gift, but now you are mad they snubbed you.