Sometimes creative conversations get heated. People get attached to their ideas, they dig in their heels and friction develops. What are you supposed to do? Dial back the heat by acknowledging the tension. It seems obvious but sometimes the obvious needs to be stated. Example, "It feels like things are getting tense. Let's take a breath, step back and refresh ourselves on the goals."
Once the tension is abated ask whether your partner is willing to entertain other ideas. Most people will acknowledge that there might be other solutions. Then invite them to help you explore them.
Another strategy for reducing the stress of competing ideas: consider listing the project goals and invite other people to help prioritize them. Often this will expose emotional attachments and focus the conversation on what is needed, as opposed to what is desired, and lead to alternate solutions.