Interested One: Great question!
You can discuss doctrine with a person who is free to think for himself. However, if you're having a dialogue with a person under the influence of Thought Reform, a person who views everything in life as being Black and White, discussing doctrine is usually pointless. Moreover, discussing doctrine with a loyal JW will (usually) trigger his cult personality. Once the cult personality has been triggered, the JW will defend things that they don't even believe in their hearts. (In other words, they will publicly defend things that, in private, they may feel differently about.)
Discussing doctrine comes AFTER you've built trust and rapport with the person. Discussing doctrine comes after the person has reached the point at which he has decided that, in fact, he could be wrong about his strongly-held beliefs.
So, if you're speaking with the authentic personality (in contrast with the defensive cult personality) and the person has admitted that perhaps WT is not God's Organization, THEN by all means discuss doctrine, perhaps pointing out some "issues" that were unsettling to you. Discuss doctrine by asking questions for which the WT literature does not provide an automatic answer to.
But, to think that one is going to visit the home of a Mormon, pull out a King James Bible or the Koran, and then proceed to convince the Mormon that his religion (and indeed his entire worldview) is incorrect, is a set one's self up for a huge disappointment.
We must also be honest about what we're up against: Those who enjoy being members of high-control groups are not going to leave. This give us two choices: find their sore spot with the Watchtower life or create a sore spot. Once the sore spot has been identified, it provides an entry point for doubt, and more importantly, Critical Thinking.
With JWs, in particular, they've been slowly indoctrinated and constantly reminded that they cannot trust (1) their own thinking ability and (2) their hearts. Stop and ponder how dangerous such a state of mind really is. What is the end result? An army of robots, many quite intelligent, waiting for the next command. Further, the WT environment constantly prepares them to outside influences, such as apostates. They are warned that the Devil (which is anything outside WT) is trying to mislead and destroy them.