The word fact means to make a model of what the fact is about. If a witness comes to the police, and the police asks for the facts about what happened, basically this means to make a model of what happened. Fact then uses a logic of cause and effect, a logic of being forced.
This is why fact cannot apply to agency of a decision, because agency of a decision is free per definition. To say it is a fact what the agency of a decision is, means to say choosing has the logic of being forced. The logic of facts, which is cause and effect, is attributed to the logic of choosing, which results in a contradiction, and the concept of choosing ceases to function.
We cannot model what love is, or hate, we can only express what love and hate are, expressing with free will, thus choosing. The brain is therefore not choosing, but it is organized for choosing, and is decided over by agency, the existence of which is a matter of opinion.