[mesmark]

I think your asking the wrong question. The question is "why is it correct grammatically?" or "Is it natural?" I believe it to be grammatically correct but not natural.

since is used here (present perfect) to define a specific starting point in the past and continues to the present. By adding the word ago you are defining the starting point (exactly 2 months ago,) therefore you can use since here (as Marylin stated.)

for is used to express a block of time, but doesn't refer to a specific starting point.

In most examples they can be used to express the same meaning.

1. I've lived in this apartment for 2 months.
2. I've lived in this apartment since 2 months ago.

If it's May, we generally assume both sentences to mean that the person has resided in the apartment since March. However, sentence 1 could mean that I lived in the apartment for 1 month in January and have lived there for another month starting in April. However, this is unlikely. Here is a better example.

I have studied Japanese for 3 years.
I have studied Japanese since 1999.

In this case I wouldn't use the second, because it implies I have studied Japanese for 6 years (starting and continuing to the present,) when in fact I began studying in 1999 and studied for two years. I stopped and began again a year ago.

As far as my "unnatural rating" of your example, it's just the long road and we generally wouldn't say it that way. That's why to us/me it sounds unnatural or awkward.

So, why is it correct? - because you defined the time in the past using ago.
Is it natural? - I would have to say it's not natural