There's a difference between you writing a poem all by yourself and you creating a character in a shared space. When you create your character for my game, you do not have 100% say so in that creation. As the DM I have the ability to tell you that no you can't be an elf since elves don't exist in my world. Your background, if any, has to be worked into the world that I am running. If you have any special ideas for your character that you want to happen, you have to run it by me and work it out. That ability means that the DM has a small measure of creative control over that PC.
If it makes you guys feel better, think of the PC like a business. You have 95% ownership of it, but I own 5% as a silent partner granted to me by the creative control that I have during character creation. So long as you are in my game, you control what your PC does and says. If you leave my game, that character remains in my world as an NPC since there is no longer a player playing it and my 5% ownership gives me the ability to take it over.