Claim: the best of an argument is the ability to convincesomeone with opposing view point.

Reason :onlu by being forced to defend an idea agaist the doubts and contrasting views of others does one really discover the value of an idea

The claim is saying that the best out of an argument comes when we try to convince someone with an opposing view point.
What is argument i ask? From my point of view it is the point over which there are different views of different people.The reason of an argument can be aythng it may be the ambiguity of the statement or its how one construes the statement.So arguments relates with the thinking of a person.The claim is saying that the best out of an argument comes when we try to convince someone with an opposing view point.

Here the claim itself serves as an argument.One may agree or disagrree with the claim and its reason,but when one needs to defend or they need to convince other his/her/their own point of view or they need to convince others they will think upon it more.They would try to come up with the ideas which support their views.When the opposing views are stronger than their views they would try strengthen their argument.Like in this example of the claim in the question, To support the claim and its reason i had to do some brainstroming activities. My aim is to convice my view to you and the only way to do it was strengthening my argument.Thus in this course of strengthening the argument i had to go through both pros and cons of this statement and thus made me realize the value of an argument.Likewise,it holds true for any argument.the success of an argument lies in convincing others our view point

Thus, when we see both the contrasting views and try to strengthen our argument side of the argument and thereby either we get convinced about their viewor they get convinced aboutour viewand thus the argument gets at its best when any one with the opposing view agrees with the oppsite view.