When disagreeing with coworkers on a design issue, I've found that it's usually a valuable exercise to bring other non-biased parties in present them with all the background information and why you both believe your solution is best, then ask their opinion. They may be other coworkers, or other designers. The key is to be open to the groups opinions and let them do as much of the talking as possible. So that it's not just one single person's opinion vs the other.
This often works, but doesn't every time. There are times that you need to just stick to your guns, but I'd be cautious you don't do this too often or you'll wear your teammates out (even if you're right). Maintaining creative team momentum is key to creating a great final product. You might get a chance to revisit this issue in the future. You don't want to forfeit flow over being right.
Another thing I've found when arguing over solution one and solution two is to make sure you're keeping an open mind — there may be a third option that you can't even imagine yet. That third option may be even better than the first two, but you'll only get there through improvisation and collaboration.