Expressions of concession and counter-argument are used in a three-part structure:
(1) there is discussion of facts that point in a certain direction
(2) it is agreed that a particular contradictory fact points the other way (concession)
(3) but the speaker/writer dismisses this fact and returns to the original direction of argument (counter-argument).
…cannot agree with outsourcing of factory jobs to poorer nations. It is true that such outsourcing may have benefited certain sections of people. Even so, it is unethical in many ways. (it is true=concession; even so=counter-argument)
Very few people actually understand what hymns and religious rituals signify. Of course, most believers know several such hymns and utter them daily, or practice certain rituals regularly. But hardly anybody can say what the hymns mean or why the rituals are done. (of course=concession; but=counter-argument)
I’m glad that you have taken up this job. It’s true that it doesn’t pay well, and the commuting time is a bit too long. Still, you are getting to do what you most love to. (it’s true=concession; still=counter-argument)
I’m not impressed by her work. Granted, she works extremely hard. But she lacks creativity.
…was incapable of lasting relationships with women. Certainly, several women loved him and he was married twice. All the same, the women closest to him were invariably deeply unhappy.
Here is a list of words you could use for these functions:
Concession: it is true, certainly, of course, granted, if, may, stressed auxiliaries
Counter-argument: however, even so, but, nevertheless, nonetheless, all the same, still