Not all mentally ill people are mass murderers

Here's a logical fallacy. You can make an assertion: "If someone commits mass murder, they are necessarily mentally ill."  But to affirm the consequent is a logical fallacy:  It does not thereby follow that if someone is mentally ill they will commit mass murder.

Affirming the consequent - Wikipedia, the free encyclopedia
en.wikipedia.org

An argument of this form is invalid, i.e., the conclusion can be false even when statements 1 and 2 are true. Since P was never asserted as the only sufficient condition for Q, other factors could account for Q (while P was false).
http://en.wikipedia.org/wiki/Affirming_the_consequent

i.e.
A  "If someone is a mass killer, they are mentally ill."

B  "If someone is mentally ill, it does NOT follow that they are a mass killer" -- that would mean 'affirming the consequent'.