Something to remember:
Just because the other guy doesn't agree with you doesn't mean he (or she) is stupid. It also doesn't mean she (or he) is attacking you. It's just a disagreement.
You may be wired -- biologically, psychologically -- to think the other guy misses all the nuances of your position, but do your best to overcome that. We're not animals here, people, even if that's the stock we come from.
Important, long, slightly depressing, but vital reading on the subject:
http://youarenotsosmart.com/2011/08/21/the-illusion-of-asymmetric-insight/