In school, we used to be instructed that, in formal writing in English, the first-person use should be avoided. However, at times, I encouter the writer using the pronoun ‘we‘; for example, ‘we would emphasize the word ‘impression‘. I mean – in what cases can I use a first-person pronoun, be it ‘I‘ or ‘we‘, in a piece of formal writing? Is there any difference in choosing ‘we‘ or ‘I‘? I never encouter ‘I‘, but I have seen writer using the pronoun ‘we‘ so many times.

*I have seen writers using

It's the same in Czech academic writing, isn't it? 🙂

I guess so. But I am not sure in what cases I can use the pronoun ‘we‘ so that it is still written in a formal register. Once I wrote ‘Let's have a look at the following quote from the book, which exemplifies the apt use of symbolism in The Tell-Tale Heart‘, and I was told it was supposed to be something without the word ‘we‘, such as ‘As way of illustration, the following quote exemplifies…‘. I was also told I should eliminate the use of the first-person while writing a piece of formal writing, such as analysis of a particular book. However, I see writers using the word ‘we‘ every now and then, so it seems a tad confusing to me.

*by way of illustration

Well, generally, if it's to be avoided, it's recommended to use author's „we“ as little as possible. But if necessary, then definitely „we“ and not „I“.
Another way is „the author of this thesis presumes…“ or sth similar.

You should also realise that in practice many rules you're taught are often broken. 🙂

Thank you. I agree with you – people do broke (even I do so) grammar rule at times. But the texts in which I saw it were texts where I would presume that they are correct (legal newsletter).

Well, I took a look again at the texts where I saw it – it seems writers use it only in those situations when they express their subjective position on something. ‘We would highlight‘, ‘we would like to emphasize‘…On the other hand, they do use the third-person pronoun while expressing something that is not subjective – ‘it is said that‘, ‘it should be noted that‘

You see – that's exactly the way I'd expect. 🙂