In many beginner material, が is said to be a subject marker. ([For example
this one](https://en.wikibooks.org/wiki/Japanese/Grammar/Basic_Particles))
However, my teacher who learnt Japanese in Japan said he has never heard such
a saying.

And in his teaching, it is very clear that が is really not a subject marker.
In many cases it is marking object instead. For example:

> 私は妹がいます  
>  I have **a sister / sisters**.
>
> テーブルの下に猫がいます  
>  There is a **cat** under the table.
>
> 私は料理が苦手です  
>  I am not good at **cooking**
>
> 私は日本語が大好きだ  
>  I love **Japanese**

These examples are just beginner level examples, right? Of course there are
also cases that が is marking the subject, but with so many cases that it is
actually marking the object instead, I wonder why there is a saying that が is
an subject marker?
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question
particle-が は-and-が
Why が is said to be a subject marker?
The particle が is referred to as a subject marker because that's what it is.
It marks the subject of a sentence. That's its primary purpose.

Even in two of the four sentences you provided, it's quite clearly marking the
subject of the verb います. Don't get confused because the "sister" and "cat" are
both objects in the most natural English translation of those sentences - the
basic meaning of います is "exist", and the sister/cat are clearly the subject of
that action. A very literal English rendering of the two sentences would be
"As for me, a sister exists." and "Beneath the table, a cat exists." - in both
of which the noun marked by が is the subject.

It's true that there are a handful of adjectives such as 苦手 and 好き which use が
in an unusual way which could be called an object role (though depending on
the analysis, you can consider even these to be subjects), but these are an
exception rather than the rule, and should be learned as such. In its standard
usage, が unambiguously marks the subject of the sentence.

The main reason why calling が the "subject particle" can confuse people is
because there's already another particle, は, which ends up marking the subject
in most sentences. However, it's important not to learn は as a simple subject
marker, because the "topic" is a more flexible concept which can actually
fulfil numerous roles in a sentence. It's just that in the majority of cases,
the topic doubles as the subject (and so the actual subject marker が is
omitted).
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answer