Firstly, the words specialty and profession are used quite differently.
Profession
a [particular occupation, business or vocation] requiring knowledge of some department of learning or science.
Specialty
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.
Could you please illustrate it with an example? is correct.
The dictionary says that Illustrate means to make clear or intelligible.
So you are asking the listener to clarify his point using an example.
Exemplify means to make an example out of. Think of it as creating an example.
For example, if I say "Federer exemplifies grace and style in tennis" it would mean I am using Federer as an example of stylistic tennis players.
So, in my opinion, an example need not be exemplified.
Best Answer
Let's start with some definitions - these all from Google as an example will reveal that technically there is not much difference between these words:
Disgusting: arousing revulsion or strong indignation.
Revolting: "causing intense disgust; disgusting"
Repulsive: "arousing intense distaste or disgust" or "of or relating to repulsion between physical objects"
Repugnant: "extremely distasteful; unacceptable" or "in conflict with; incompatible with."
Now...
Disgusting to me brings up an idea of a sickening feeling in your stomach. Though of course it is used to describe many things other than food, smells, etc. It comes from a French word meaning "taste" (dis- being a negative prefix).
Repulsive is derived from repel (Latin) which means to push away.
Revolting is derived from Latin revolvere which means to "roll back."
Repugnant to me immediately brings up an idea of a bad smell. This is from a French word meaning opposing.
So really, repulsive and revolting are about the same exact thing. Disgusting is more about a physical sensation than a general want to be away from something. Repugnant means to reject something strongly.
To be honest though, none of these words (at least by themselves) are strong enough to describe something that is among the worst things that has happened in human history, and the netural word "actions" would make any word weaker in that regard.
I would call this an atrocity (pl. atrocities), and a word to describe could be horrific.