What does put the argument into a concrete shape into an image some hard phrase round and solid as a ball which they can see and handle and carry home with them and the cause is half won mean?

Answer 1

It means that in any argument, you have to pare down the main ideas and points into something easy to understand. By easily understanding the argument a person is more susceptible to thinking about it and to applying the basic parts to their own life.

The idea behind the phrase is that an argument is intangible by nature and therefore difficult for people to perceive. By making it tangible, or concrete, people are able to easily see it, understand it, and contemplate it.

Answer 2

This means that by presenting an argument in a clear, tangible way that people can easily understand and remember, you have already made significant progress in persuading them to see your point of view. When you make your argument solid and relatable, it becomes easier for others to grasp and consider.