A counter-argument is an argument that goes against the author’s main conclusion. Typically, counter-arguments are considered and rejected in an attempt to strengthen the author’s case.

For example, “If Superman and Spiderman had a fight, then Superman would win as his ability to fly would mean he could attack from any angle. You might think that Spiderman’s ability to hurl webs (a ranged weapon) would give him the edge, but Superman would be manoeuvrable enough to dodge them.”

In this passage, the main conclusion is “If Superman and Spiderman had a fight, then Superman would win”. The reason given in support of this is “his ability to fly would mean he could attack from any angle”.

Also considered, though, is an argument that Spiderman would win: “Spiderman’s ability to hurl webs (a ranged weapon) would give him the edge”; this is a counter-argument.

It is then dismissed with the comment “Superman would be manoeuvrable enough to dodge them”.