Firstly, the words specialty and profession are used quite differently.
a [particular occupation, business or vocation] requiring knowledge of some department of learning or science.
a special subject of study, line of work, area of interest
A profession is very broad, you can be a policeman, a doctor or a software engineer. A profession requires knowledge and study, but is very broad. A general understanding of computers is rarely described as 'a specialty'. Also a profession can be even broader such as "technology".
A specialty is very specific, for example a homicide detective, a neuroscientist or a java developer. This is a doctor that "specializes" in neuroscience.
then please let me know what a native speaker would say in a natural way to indicate exactly the same message.
Both are valid, however I would probably use something like:
I can do this because it falls within my area of expertise
I can do this because I am qualified to do so
My training qualifies me for this task.
The reason that I would use phrases such as "area of expertise" is that this is indicative of a human ability. "Profession" is quite broad, but you could say that "I can do this because it is my job, I am used to doing it". "Specialization" is very narrow and not really used colloquially "I can do this because it is my specialty" is grammatically correct but I've never heard it used. I think perhaps because it is a fundamentally academic word, you specialize in medicine, and this is used frequently in an academic context.