When you find two doctrines that are in apparent conflict you need to take a look at both of them. Are they in conflict? Where do they originate? Is it in the scripture or is it in psychology, mystical books, tradition etc. If it's not in the scripture then it's likely not very important.
Jesus said to beware the yeast of the Pharisees. Yeast puffs up bread and creates voids. Basically it's the addition of things that seem to be substance but is in fact just air. The problem is that once you start down this road it's really impossible to determine truth because you no longer have a basis for truth.
The Bareans were noble and looked at the truth of the word to see if Paul was telling the truth. This is real nobility.
With respect to doctrines like predestination vs Armenian thoughts we should look to the scripture. If I look at one and then look at the other am I going to find that one is without basis in scripture. Do I need to ignore some scripture in order to believe one?
Solomon was right when he said "the end of the matter is to fear God and keep his commandments".
For me the only doctrines I research and want to know more about have to do with are they going to help me to obey, fear, trust or in any way please God? If they are not then I am not interested.
How does predestination vs choice affect my obedience, love, fear, etc? What scriptures do I get to dismiss and not obey because of one or the other. If it doesn't empower or encourage then I am just not interested in it's pursuit.
I only have so much time in any day and none of it's available to research on matters that are only going to be used to answer question on trivia games about Christianity.
I don't want a trivial life so I won't spend it on trivia. Yeah, I said it.
I would say much much more about the people who do specialize in the trivial and are great debaters that just ruin the listeners. It's because they don't really care about their listeners that they debate. They care about being and looking intelligent. Leave them, pray for them but don't let them waste your time or life.