I have difficulty accepting the subjectivity of my own logic as well, but at the end of the day all Ti reasoning is arbitrary and internal. If it's uninfluenced by external conditions, it's subjective, regardless of whether or not it's based on personal emotions.
The use of the terms subjective/objective in that MBTI test question is erroneous--just another mistake in a poorly designed testing system for a concept that can't be tested empirically. When they say subjective/objective, they really mean personal/impersonal, which is not the same thing. The use of "subjective vs. objective" as a description of F vs. T is a common error, but an error nonetheless. Ti's judgments are less personal and less emotional, but that doesn't make them any more objective than Fi's.