Healthy conflict
We're usually taught to avoid conflict, but sometimes conflict can be good when it's properly handled. For instance, at work, when there's disagreement and people are invested in their suggestions, it means they care. It's a bit controversial and shouldn't be confused with being stubborn. However, showing interest in something is a good sign.
Now, the way conflict can be beneficial is that all parties make an effort to understand each other. They don't have to agree, just listen to the other side. Ask questions about their motivations and explore what-if scenarios. Once all the information is at hand, the decision-maker (usually the person responsible for the task) can make a call.
It might not be easy for the party that didn't get their way, but it's important to commit and move on. This ends the conflict and, more importantly, allows for execution and the observation of results. The decision might not be perfect, but as long as it was made with all the information available, executing on it now will get you closer to the truth.