I have seen many variations of this question by exmos on various sites, and I have asked myself this question repeatedly. Unfortunately, I think the truth is that you can't. It doesn't matter what kinds of historical citations you have or what kind of personal experiences. It doesn't matter if you can point out contradictions in belief, or show contradictory statements. It doesn't matter if you are completely logical, reasonable, knowledgeable, objective, patient, and clear. You cannot follow an agenda or checklist that will prove to your family and friends that you are right.
Why? Because it is your friends and family who decide what to conclude about the information you present. No matter how you present the information, and no matter how persuasive that information is, it is still up to the person themselves to decide what the information means. Opposing conclusions often lead to conflict.
You expect that when exposed to the same information that led you to certain conclusions, your family member or friend will come to the same conclusion as you. (This idea is solidified by the many other exmos you have talked with who have come to the same conclusions as you.) When the person doesn't agree with your conclusion, you push the information harder and repeat yourself. This only makes the person disagree more strongly. Even if the conversation doesn't escalate into an all-out brawl, it will still probably end with both sides feeling angry and frustrated.
How can you avoid feeling angry and frustrated when discussing a sensitive subject like religion with someone who sees things very differently? First, you have to reconsider what your goal of the conversation is. Is your goal to get the other person to admit that she wrong? If it is, you are guaranteed to fail. No one can be forced to admit anything, and they are more likely to disagree with you, simply out of spite, if they see you as an aggressor or enemy.
Have you considered the goal of having the other person understand your perspective?
