There are many reasons for business jet ownership (or private aircraft ownership in general) other than to "show off".
Convenience, flexibility, and privacy, to name a few. Also many business jet owners are pilots themselves. Many enjoy the personalized service -- flying with the same friendly crew for years.
One of the first companies I worked for did a lot of business in remote areas in a different state, not served by any airline nearby. Our CEO often flew the company plane himself for meetings, site inspections, etc. I've flown right seat a couple of times.
Much more convenient and efficient than two days in a car each time. And time does equal money.