One of the reasons to use evidence when speaking to persuade is that it can make your listeners more resistant to counterpersuasion.

It is true that you would need evidence in order to have an argument that would be difficult to rebut or counter argue. This is because the presence of evidence in argument establishes the truthfulness or the likelihood of it happening in the real world.

This is very true. The more (reliable and reputable) information that a person can give to bolster their claims, the easier it is to persuade the audience. In addition, it leaves fewer openings available that can be rebutted against by someone else making a counterclaim, which could be used against the first speaker to weaken his or her original premises.