This is a good point.

The minute the car honked, you didn't need to look back but give him/her more room. Even if you did have the mirror, cars will still honk regardless. If you're in the door zone, cars will still honk! Being able to keep the front wheel steady when a car honks is an important skill you'll just have to master.

In your situation, what was more important than looking back was giving the motorist more room. Most will expect you to ride in the door zone which is dangerous. There are times when you have to take the lane and if means being honked, so be it. More room is all he wanted and you have to make the decision on if it's safe to give him the room or not. The mirror will not stop the honking. Get used to it.

The only thing the mirror will do is you'll be able to see his angry face after he honks the hell out of you!