Illicit observation is one of the many smokescreens that are used to cover the fact that the reasoning is based on one of the three fallacies of Agrippa's trilemma. Whenever a logical fallacy is committed, the fallacy has its roots in Agrippa's trilemma. All human thought (without Divine revelation) is based on one of three unhappy possibilities. These three possibilities are infinite regress, circular reasoning, or axiomatic thinking. This problem is known as Agrippa's trilemma. Some have claimed that only logic and math can be known without Divine revelation; however, that is not true. There is no reason to trust either logic or math without Divine revelation. Science is also limited to the pragmatic because of the weakness on human reasoning, which is known as Agrippa's trilemma. This is a fallacy that superimposes another level of fallacy on top or one or more of the three fallacies of Agrippa's trilemma.
The Illicit Observation Fallacy occurs when two terms are used in a way that implies that one negates the other but they don't or that they are opposites when they are not. This fallacy often involves that distinction between contrary and contradictory terms. This is a type of ambiguity fallacy.
Examples of the Illicit Observation Fallacy
"You have to make a choice between faith and science."
"You have to make a choice between faith and logic."
Faith doesn't negate science and faith doesn't negate logic. Faith is necessary for both science and logic.