How do I explain and defend my design process to the people I work with?
"I find it hard defending the design process and execution of my designs to a team of marketers/project managers/developers. What can I do to make this easier?"
You have to explain how the design is helpful to them. You are the designer and you are designing for a specific target audience.
If your designs resonate with that target audience, it makes their job easier. It wasn't designed with them in mind and if they don't get it, that's fine as they are who it is intended for.
You'll have to be patient and take them through your decision making process. But remember, you are the professional designer, not them. They shouldn't tell you how to do your job, as you don't tell them how to do theirs.
It's all about respect and open communication.