Resolving Disagreements - Effective Communication For Engineers

Your goal with a disagreement isn't to prove that your side is correct; it's actually the opposite - Try to tear down your own argument.
Don't view the situation as a "Us vs. Them" mentality. It's not a debate that you have to "win". If you come in with this mentality, the other side will respond in kind, and you will never get anything done.
Acknowledge the operating principles and incentives of the other side, and try to weave them into your approach as well.
Example: Your designer proposes beautiful but overly ambitious design that cannot be done on the current aggressive build timeline.
- Bad: "We don't have enough time to build these designs, so let's toss them out."
- Good: "These designs look amazing! However, the timeline is pretty tight, so we may not be able to get everything within them. Can we get the low-hanging fruit with this intermediate state design to hit the ship goal, and then we can get the remaining design extras as a fast-follow? I really want to bring all these aesthetics to life, but I want to make sure we hit the deadline as well."
Be comfortable with compromise and reaching a middle-ground that imbues something from both sides. It's possible that the other perspective is completely incorrect, but this will be very rare as people in tech are generally pretty smart. You should very rarely treat your approach as one where compromise cannot be made at all.