It goes by many names–the false dichotomy, the either/or when you should be thinking both/and, first things and second things. We have a mental weakness–we’re fine with exposure to various ideas, but we want them to combine into perfectly harmonized chords.
Perhaps we should be trying to synthesize ideas rather than to harmonize them. To synthesize literally means to put together; we’ve added a connotation of putting things together in a way that makes sense. To harmonize ideas is to make them fit together. The problem is, ideas aren’t always mutually consistent in themselves; they may each be true within specific contexts or in specific ways. Sometimes, we simply need to hold several mutually inconsistent ideas. Don’t force them to premature consistency; don’t stop asking why they seem both true and inconsistent, or on what underlying framework they both might fit.
When two ideas are in conflict, consider that the “opponents” may actually be on the same team, but playing by rules you don’t yet know. You have a deep framework, a network of ideas that makes up who you are. Some ideas are easily wired into the structure; others require a lot of reorganization. As your framework gets more complex, you gain in ability to process ideas. Apparent conflicts are a gift, forcing you to increase your mental abilities in order to handle them. Embrace this chance to grow.