Argument in this context is 'what your essay is trying to say." Support is evidence and reasoning that explains why you believe your argument is true.

It's a little unclear because there's no examples. But normally it would be: your argument Counter-argument Your conclusion Perhaps here ARGUMENT means the counter-argument Gun control would result in fewer suicides (argument) Gun control would have no effect on the number of suicides, as people would find other ways of killing themselves (counter-argument)