I would just like to add the slightest bit to the excellent answer above.
If you need a rationale or another way to think about the use of "I" in an essay, you should normally avoid using "I" because doing so is wordy. When the reader already assumes whatever you express is your opinion, because your name is on the essay, using "I believe..." or whatever, is wordy.
For years teachers (at least some) taught that it was incorrect to use "I" in an essay, until research showed that professional writers use it quite often. There is no good reason to completely prohibit the use of the first person. But, again, most of the time it is wordy, and thus should be avoided.
Yes, you certainly can use "I" in an essay, but generally it's better not to. Many teachers don't like the use of "I" at all, even in a polemical essay. (The link given below, for example, states: "Using the first person weakens your argument.") Instead of writing "I believe that this evidence is unconvincing," these teachers would probably suggest that you should write "This evidence is unconvincing." Unless this statement is clearly attributed to someone else (e.g. "Many experts believe that this evidence is unconvincing"), readers should understand that this polemical statement is coming from the writer (you).
At the same time, however, I think there are some very effective ways in which to use "I" in a polemical essay. For me, it's often important in an argument to express your perspective on the issue, and your perspective is always closely tied to who you are as a person and to what you have experienced in life. You may have personal experience to draw on, for example, or you may belong to a particular group that is involved in the issue that you are discussing. For example, I could write a polemical essay on how Americans are the cause of all sorts of problems because they are often overly eager to sue and could briefly explain my own experience of being driven off the road by an 18-wheeler yet choosing not to sue. Just because I've experienced something, of course, doesn't make me the ultimate expert, and every experience is different. The best I can do in any argument, I believe, is to explain where I am coming from and present the evidence as I see it.
In short, you definitely should not use "I think that..." or "I believe..." at the beginning of every sentence in your polemical essay, but you may find it useful (for both you and your readers) to articulate your individual perspective (using "I" when necessary) of the topic that you are discussing.