Conflict between ideas is inherent in the ideas themselves. It's not a matter of belligerence, of attitude, of the personalities involved. There are points of conflict that are demonstrable, where each idea contradicts the other. If one is true, the other must be modified, possibly discarded.
When we become aware of a conflict between ideas we hold true, or a conflict between ours and those of another, we have a choice.
We can address the conflict: emphasizing the point of contradiction, explore how each idea's validity can be supported with reference to either A) observable reality, or B) some acknowledged truth, fundamental to both parties' understanding. B is usually best and easiest, but if the parties can find no fundamental shared truths between them, relevant to the ideas in question, they can still fall back upon A. If neither idea can be supported from there, any conflict between the ideas is probably imaginary.
Or, we can elect to leave it unaddressed. Whenever we become aware of a conflict between ideas and we fail to address that conflict, this is either cowardice or apathy. Cowardice, when we doubt our ideas can stand up to the examination, and we fear the consequences if they are undermined. Apathy, when we don't believe the attempt is worth the effort.
Don't worry. In either case, the attitude is probably entirely justified.
In neither case is anything of one's self at risk. When an idea of ours is undermined, the worst that can happen is that we become motivated to explore it more deeply, eventually to reach a better grasp of it. The better to hold it, if the idea is fundamentally sound.
Sometimes, the only better grasp we can get of an idea is to let it go. No harm done to anyone. If we ever want another look at it, or if we're feeling nostalgic, we can always wander back to the idea later and pick it up, kick it around!