Guidelines for Engaging in Discussions
I'm aware of a few guidelines in arguing with a person.
First, at all costs maintain your calm and keep yourself in peace. No matter what verbal or written attacks may be launched against your person or ideas.
Second, if the person is not arguing rationally, then you should 'break contact' because in their irrational state any logical arguments that you may put forward will only cause the person to hold to their irrational beliefs with greater tenacity.
Second, what out for challenges in which there are a number of undeclared assumptions. If these are not made explicit there is a risk of answering the question but not the assumption.
In face-to-face confrontations, it necessary to move from the 'artifacts' to the 'beliefs' and 'assumptions' in order to determine what motivated the attack or challenge.
In this manner, you can shift from the multitude of challenges that can be brought forward and move to the real issues and beliefs that they are defending when they attack / challenge you.
When confronted with a written attack/challenge, the task is a little easier, as long as you pause to reflect upon the statement made.
In this case, I suggest simply setting aside the statement (email or whatever) for a later review when you can be more objective.
Once you're ready, take the offending statement and pick it apart - piece by piece - examining it first and foremost for undeclared assumptions.