As a(n) noun vs as only
I wonder about the use of as a and as (only) in writing. Can you explain when it is correct to quantify the noun when presenting oneself? I will paste some examples for clarity.
Are there any rules to follow?
Example 1
a) As teacher, I meet many children.
b) As a teacher, I meet many children.
Example 2
a) Working as pilot, I fly airplanes.
b) Working as a pilot, I fly airplanes.
In Germanic languages, like your (presumably) native German and Swedish, you avoid indefinite article for professions. However in English they are present. So in your case, "as a teacher, ... " should be the right form. Here's a ngram plot to support the idea.
Here's an interesting article on definite and indefinite article use in English, compared to some other languages, among which German. Note the following quote:
Although greatly simplified, English article usage still poses a number of challenges to speakers of other European languages. Let's compare the German sentence "Da er Botaniker ist, liebt er die Natur" with the corresponding English one "Being a botanist, he is fond of nature". You'll see that English puts an indefinite article in front of a profession but German doesn't. Conversely, English manages without articles in front of abstract nouns like nature, where German needs a definite article.
So far as I can see, OP's example 2a could never be valid. 1a requires a very specific (slightly contrived) context to be "valid/natural", which might be easier to see if we consider...
1: As breadwinner, I don't make quite enough money to support myself (or my family) in this job.
2: Dad had some hang-ups about his working wife taking away from his role as breadwinner.
In both the above contexts (which I consider to be perfectly well-formed sentences) it would be quite acceptable (but not required) to include the definite article ("the"). That's because of the pragmatically strong implication that there's only one breadwinner in the current context.
3: Besides myself, the only other people employed by our tiny village school are the groundsman, the cook, and the part-time secretary. So as [the] teacher, I get to meet the parents of every pupil.
In (3) above, using the indefinite article ("a") would be extremely unlikely, if not actually "invalid". But as a general principle, if using the definite article would be credible, it's also possible to omit it.
Assuming OP isn't a native speaker, the "correct" answer for the most common context is Include the indefinite article. But if that's all that's being asked about, perhaps the question should have been asked on English Language Learners.