Cadfan,
What if the DM realizes that his dislike for dragonborn will ultimately have a negative effect on the quality of the game he runs? If the presence bothers him, every time the character comes into play, the character is a reminder of how much he dislikes that race. It's reoccurence and having to make accomodations for it when he designs adventures, when the PCs interact with NPCs, etc. results in DMing becoming unfun and a chore. When, DMing becomes unfun, the game as a whole suffers in quality and probably dies often resulting in no game for anyone (if we are to believe the disproportionate number of players to dms).
1. Why is this concern unique to the DM? What if the DM hates dragonborn, but loves tieflings, and one of the players knows that his hatred of tieflings will ultimately have a negative effect on his contributions to the game?
If your argument is that the DM is more important, so he has to be mollycoddled more than the players because his unhappiness will reverberate in a way that a player's will not, are you really happy with that reasoning? With the idea that the DM is essentially a giant baby, and everyone has to be extra nice to him and give him privileges that no one else gets not because he will use them more wisely, but simply because catering to him is the only way that everyone can get along?
2. I question whether this really happens to people. See my earlier post about actually hating something so bad it makes the game suffer, and just being dramatic. IF the DM hates something so bad the game will suffer from his primal revulsion, THEN that something should probably be banned (or the DM replaced with someone a little less emotionally fragile), BUT I think it is very unlikely that most people actually hate something like a player character race quite that much.
I'm amazed how much disagreement my views generate. I just think that the reason that we respect the DM's authority is because he is in a position to best decide whether adding dragonborn to the game will help or hurt the overall game experience. I think the respect that the DM is entitled to is tied to this superior perspective, and is therefore forfeit if the DM abandons that perspective and starts using the authority vested in him by the group to satisfy personal whims unrelated to the quality of the game.
So, I respect the decision of a DM who bans something for a game related reason, and I don't respect the decision of a DM who bans something because he thinks its stupid and he knows he can get away with banning it because the players will let him have what he wants rather than try to find a new DM.
I don't see why that's so controversial.