From his perspective, it doesn’t make sense to spend billable hours to fix his own car. From your perspective, it creates the impression that he will never go the extra mile. As a customer, you doubt his abilities and professionalism. The fact that his own car is broken has nothing to do with his abilities, or does it?
You need to showcase the work you want others to pay you for. What better place to start than consuming your own products. Those hours might not be billable, but they pay more than their dues in marketing collateral. It showcases the passion you have for what you do. It proves the quality of your work.
Find ways to show your work. If no one is willing to pay you for it, pay yourself.
I have never seen a Ferrari outside the workshop of a mechanic with a broken car.