There are definitely times when you need the title to make meetings happen, so it's not a sure-fire guarantee of arrogance. But it's still a warning sign.
At the last startup I founded, both myself and my co-founder agreed to skip titles until such time as they were required. When pressed, we were both just 'founders'.
Professionally, I am a farmer, a programmer, a designer, an administrator, and was even a baker for a short while; though, sadly, I gave it up as it was too time consuming on top of the rest. Not to mention all of the business stuff that goes along with doing those jobs, like management, sales, mechanic in the case of my farm, etc, etc.
Why are people so hung up on them? They are pretty meaningless.
I worked for a government agency for a long time. At one point of my career, bigshots at the director level would not acknowledge my presence in a room. Later, they were my best buddies, because I was high enough on the ladder to be a minor "player" to potentially influence one of their peers.
I don't even know what I do for a living, I just work on what needs to be done or feels right at any given time. My job is to solve problems and create value for others, just like everyone else. You can't be more specific than that.
Corporate titles sound silly in small businesses -- I had my driveway sealed by the "President and CEO" of a driveway sealing business the other day.
People in contact with customers should have flexibility or use multiple titles. If you're trying to get an audience with a Managing Director or a Deputy Commissioner in government, shitty titles won't cut it. An "Account Manager" won't get past a secretary, but "VP of North American Sales" might. In other contexts, the dramatic title is a liability.