These seems like conflicting instructions. When you are "objective" you shouldn't let your personal opinion influence you, as opposed to be ing "subjective," when your personal opinion does show.
If you are supposed to write an essay that convinces me of your opinion, then obviously you have to make it clear what your opinion is.
However, you can still use a factual, objective basis to show the validity of your point of view.
Let's say that you are in charge of evaluating a lot of resumes to determine the best candidates to bring in for an interview. You don't know any of the people, so you have no emotional connection to them. Instead, you look at their experience, education, how well their cover let shows that they understand the job - these are facts, or reasoned opinions, and therefore can be an objective treatmean of your topic, even while you try to persuade me that they are the best candidate to interview.
You could do the same with a recommendation for which stove is the best choice for my house, using facts like energy use, cost, etc.
I don't think you can do that for a movie, though - that does have too many non-factual elements. Nor could you do it for an essay that's supposed to persuade me to give money to your favorite charity - that DOES require an emotional connection.