Multiple choice test has the perception of being objective because it's not graded by a teacher, who would considered to be subjective. But you have to think about the person who came up with the questions, the way the questions are phrased and the 'distractors', which are the answer choices, they are all written with someone's subjective views.

It's also difficult because the person who writes the question has his/her own culture and an unique perspective on a certain matter and that's 'subjectivity' right there. Same applies for someone who are creating the 'distractors'.