So, in an essay, one is not supposed to use first or second person pronouns, of course. But I recently made the mistake of including "Many of us today..." which my teacher told me I should change to avoid the personal pronoun usage. My thinking was that I was using the 'we' in an impersonal way, referring to people in general rather than 'you and me' specifically. I know I wouldn't be able to convince him to allow this even if this usage is correct, but this question has piqued my curiosity. So, can 'we/us/our' be used impersonally?
"We tell ourselves stories in order to live."
This is the first sentence in an essay titled "The White Album" (in a book by that name) written by Joan Didion, who is considered an excellent American stylist.
The question to ask yourself when we/us/our are used in an essay is who is "we"?
In Didion's essay, she is speaking of everyone--all people. She goes on, a few sentences later:
"We live entirely, especially if we are writers, by the imposition of a narrative line upon disparate images, by the 'ideas' with which we have learned to freeze the shifting phantasmagoria which is our actual experience."
Another essay in the same book begins:
"Some of us who live in arid parts of the world think about water with a reverence others find excessive."
Here "we" (us) refers to a subset of all the people who live in dry regions; Didion limits the scope to "some" of these people.
If a writer of an editorial for a newspaper says "We disagree with the position of the administration on this policy," "we" refers to the editorial staff of the newspaper. This is literally the editorial "we".
If a European politician (say, Angela Merkel) says "We favor XYZ," she may be speaking on behalf of her country or perhaps of the European Union. It is likely that she will make clear on whose behalf she is speaking.
A spokesperson for a government administration (US, British, whatever) will use "we" to express the position of the administration: "We support this legislation."
If I as an author write about the need to strengthen our national defenses, I am implicitly speaking to citizens of my country about my country's national defenses. This is an error. I should have said, "The United States needs to strengthen its national defenses."
On the other hand, if I give a political speech and say, "We should elect candidates who will be concerned with our goals and aspirations," I'm implicitly talking to an audience (in the room or not) who are potential voters in the place where I'm a voter. "We" is appropriate here because I want to identify with the audience and gain their support.
As Azuaron's answer points out, an impersonal reference requires a phrase like "most people," "many people," "some people," modified any way you like.
The co-authors of a joint article (or often a single article) for a scholarly journal often find it inconvenient to avoid referring to themselves as "we". But essays (editorial, op-eds, magazine stories) are more expressive and free stylistically. Nevertheless, it's always important to figure out to whom "we" refers.
Since you asked for an opinion in the comment to your question, I'll offer mine here.
The important thing is consistency of tone, so that a shift of tone will mean something to your reader. For example, a tutorial paper in mathematics might use "we" to carry the reader along on a "journey of discovery", but then step back to third person to make a comment, e.g.
We combine Equation 1 with Equation 2, and solve for the position of the aircraft...
We then substitute the position into our antenna-pointing formula...
At this point, the reader might wonder how often the antenna actually has to be repointed, and here the authors can offer some real-life examples...
A shift from third person to second or even first person can be like an actor making an aside to the audience. For example, in the opening to the 1969 James Bond film On Her Majesty's Secret Service, there's a memorable moment where the late George Lazenby breaks the "fourth wall" and speaks directly to the viewer: "This never happened to the other fellow." It works in part because it's completely unexpected, although there are plays and films where asides are more common, and the audience expects them.
It's not something to be overused, though, which may be why your instructor made the comment that they did. It's easy for us readers to get confused.
We/us/our cannot be used impersonally. Your teacher isn't asking you to use a different form of the word; your teacher is asking you not to refer to yourself or the reader/audience.
Assume this was your statement:
Many of us today are human.
Change that to something like this:
Many people today are human.
By saying, "Many people," you still get to convey the idea you want, but you are doing it in a more formal manner that does not assume an audience or an audience that is familiar with you.