: Is using first person in academic/technical essays always bad? For as long as I can remember, my teachers have taught me never to use first person in an essay. Yet, some of the examples

The restrictions on 1st person (singular or plural) does depend on:

The genre of writing
The style guide being followed
The opinion of the teacher/instructor/advisor/publisher/editor
The context within the paper

Genre of Writing
Generally speaking, it is research writing that tends to favor not using 1st person. The reason for this is that research ought to be objective, not subjective, and too many inexperienced students (i.e. college undergraduates or younger, though even some graduates) doing research writing tend to write opinion, rather than properly researched and documented facts. So for these types of students, it is often safest for a teacher to say avoid 1st person. This helps force the student not to be thinking about what they "believe," but rather what they can "prove" via their research.
Style Guides
Style guides vary on what is allowed, but generally have some similar ideas. For instance, The Concise Rules of APA, 6th edition (2010) states for an appropriate use of 1st person (bold added):

Innappropriately or illogically attributing action in an effort to be objective can be misleading. ... To avoid ambiguity, use a personal pronoun rather than the third person when describing steps taken in your experiment.  Correct:    We reviewed the literature.  Incorrect:    The authors reviewed the literature. (sec. 1.09, pp. 19-20)

But then further clarifies use (bold added):

For clarity, restrict your use of we to refer only to yourself and your coauthors (use I if you are the sole author of the paper). Broader uses of we may leave your readers wondering to whom you are referring. (sec. 1.09, p. 20)

So in short, don't include in a "we" (1) the readers, (2) other people in the field of study who did not author the paper with you.
Similarly, A Manual for Writers of Research Papers, Theses, and Dissertations, 9th edition (2018), which tends to follow The Chicago Manual of Style in a lot of respects, says the following about avoiding 1st person (bold added):

Most instructors and editors do agree that two uses of I should be avoided:

Insecure writers begin too many sentences with I think or I believe (or their equivalent, In my opinion). Readers assume that you think and believe what you write, so you don't have to say you do.
Inexperienced writers too often narrate their research: First I consulted ..., then I examined ..., and so on. Reader care less about the story of your research than about its results. (sec. 11.1.7, p. 120)

And then later notes two more with respect to the 1st person plural as well:

But many instructors and editors object to other uses of we:

the royal we used to refer reflexively to the writer
the all-purpose we that refers to people in general (sec. 11.1.7, p. 121)

Between the above inappropriate uses, the manual notes some positive uses:

The first person is appropriate on two occasions ...

An occasional introductory I (or we) believe can soften the dogmatic edge of a statement ... The trick is not to hedge so often that you sound uncertain or so rarely that you sound smug.
... when it's the subject of a verb naming an action unique to you as the writer of your argument. Verbs referring to such actions typically appear in introductions (I will show/argue/prove/claim that X) and in conclusions (I have demonstrated/concluded that Y). Since only you can show, prove, or claim what's in your argument, only you can say so with I. ... On the other hand, researchers rarely use the first person for an action that others must repeat to replicate their research. Those words include divide, measure, weigh, examine, and so on. ... Those same principles apply to we, if you're one of two or more authors. (sec. 11.1.7, pp. 120-121)

Authority's Opinion
Style guides give some "allowance," but whoever an author is writing for has ultimate say on what precisely is allowed. This is generally noted in the style guides as well.
For instance, the second bullet point in the preceding quote about "appropriate" uses would not be a valid use by a number of people in authority who believe such metadiscourse (or signposting) that gives a discussion of what the author "will do" in the paper is bad writing for a couple of reasons: (1) regarding whether an author "proves" the point or not is up to the reader, whether the author believes it was proven or not; (2) what the author is showing, arguing, claiming, etc., should be evident within good writing without it being explicitly stated.
The point, however, is that the one the author is writing for (whether a class or a publication) determines the appropriate uses of 1st person; the author just needs to follow the rules laid down.
Context within the Paper
This relates directly to the caveats noted in the style guide section above, and also relates to the authority's acceptance or not. Some places in a paper may be appropriate to use 1st person, other places not. If an author is giving a personal illustration, it would be appropriate; but in a research paper, a personal illustration is generally not often used (since it cannot be verified; it is subjective). So whether or not it is allowed in a particular place will no doubt depend much on the context within the paper itself.

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It depends on what your goal is. If your essay is supposed to say something about the world in general, you should maybe avoid the first person, because that could make it seem as if your essay's conclusions are based on a sample size of one, which would detract from its validity.

On the other hand, if you want to share something you personally accomplished, or discovered, or witnessed, then using the first person could add validity to your essay, because hey, you were there, right?

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I will try to convey the request and explanation of one of my professors. He specifically asked me to change generic speaking to 1st person singular.

(His) explanation:

It is OK to use generic speaking or 3rd person if you talk about
something that is generally known, or it was published / researched by
somebody else. But if you describe your own work, it is confusing to
use anything else than 1st person singular.

It was very reasonable (and very awkward - to learn to take responsibility and credit for my own work), but it became my own thinking meanwhile.

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Like with so many other issues of style, it depends on your audience.

For a school essay, your audience is your teacher. So write the essay your teacher wants, no matter if it's okay to do it another way elsewhere.

If you submit an essay or article for publication, the audience is the publisher, and you should follow its rules. A publisher curates for a larger audience and will have rules and expectations for authors that fit those needs.

Some academic essays need to be in first person. Imagine a college application essay written in 3rd person. I'm sure people have done it. I wouldn't advise it. If you're writing an essay to read out loud at a conference or other presentation, and it's about your work, you also need to use first person or it's just weird and confusing.

Figure out your audience and adjust your writing accordingly.

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This depends on your style guide and potentially your teacher/school/boss/etc.'s guidelines. If your teacher (for example) says to avoid using the first person you may be able to negotiate to change their position, but ultimately they are the ones evaluating your work so you need to follow their rules.

None of the three major American style guides forbids using first person.

This is what the APA Blog has to say about the first person:

I am often asked why APA Style prohibits the use of I or we. I love this question, because the answer is always a pleasant surprise: I or we is perfectly acceptable in APA Style! In fact, the Publication Manual actually recommends using first person, when appropriate, to avoid ambiguity.

(Another APA blog post also addresses this issue.)

According to a Q&A on the CMOS website, the CMOS says this:

Please see CMOS 5.220, s.v. I; me: “When you need the first person, use it. It’s not immodest to use it; it’s superstitious not to.”

Another Q&A on their site says:

Avoiding the first person used to be considered proper, but now it’s considered very formal, if not old-fashioned. It’s not a question of correctness, however; both styles are correct. If you feel strongly that the first person is out of place in your work, don’t use it.

MLA, on their webpage, says:

Let the first-person singular be, instead, a tool that you take out when you think it’s needed and that you leave in the toolbox when you think it’s not.

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My recommendation is to use first-person pronouns only for attribution. If you do something original, such as a thesis or other research, it makes sense to use "we" for things you did with your supervisor, or "I" for what you managed on your own. It's important to examiners/reviewers to know what is one, what is the other and what is instead due to previous academics, and to be confident of your non-plagiaristic honesty on that front. Laurel's answer shows a number of style guides for such writing gives similar advice.

If your essay contains nothing original, such as when you give an overview of the arguments for and against philosophers' views on an issue, the fact you wrote the essay is immaterial, and you should effectively be as anonymous as a Wikipedia article's author(s). Although you don't go into detail about where you read an author using "I", my best guess is it was when they made a case for something of their own.

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