In the "House Divided" speech, Abraham Lincoln makes a prediction about the government of the United States. He tells us that he believes the country is unable to survive division. It cannot go on with half of the country accepting slavery and the other half outlawing it. Therefore, he predicts the country has to settle on one or the other.
Lincoln tells us that this debate is similar to the process that riders have before mounting a horse. He states that some riders pat and pet the horse because they are scared the horse might "give them a fall." However, he argues that this is a pointless and futile pursuit, much like that of defending slavery. The purpose of the analogy is to present, in simple terms, what the role of slavery should be in the Union, and how the effort to preserve it is bound to fail.