But the standard is the person who killed so, was it reasonable for a person suffering from a severe anxiety disorder to belive that his wife, who he just had a normal argument with, to belive that wife was about to kill him?
No, it would not be reasonable. Reasonable in a legal sense is based on what a "reasonable person" would believe. Hence, the fact that they use the word "reasonable" says that the law isn't like you are presenting here.
Although a "insanity" defense might be applicable, this would not be a "self-defense" killing as the "reasonable person" standard would not apply.