"General Manager" gives you a lot of flexibility to be what you need to be to different people. If you're CEO, COO, etc, it's harder to say during a negotiation "I've got to check with so-and-so and I'll get back to you" to cool things down. Lower titles obviously convey lower authority for people who want to speak to someone higher up.

Source: A mentor of mine who runs one of the most profitable architecture firms in the Middle East.