The main types of literary conflict are often listed as follows:
- Man against man / man against society
- Man against himself
- Man against Nature
- Man against machine
- Man against God / gods / fate
The word "Man" here is used to mean any human being, so it simply means the protagonist(s) of the story, whether man, woman, or child.
Of these categories, The Swiss Family Robinson fits best in "Man against Nature."
Man against man is probably the most common type of conflict found in literature. It is found in crime stories, war stories, and so on. Also, almost every story includes some type of man against man, even if it is not the main conflict. The Swiss Family Robinson is somewhat unique in this way. The family are never threatened by human enemies from without. They do not even encounter any native inhabitants of the island. And although there is sometimes a little bit of (hinted) friction between family members, it never becomes a main part of the story.
Man against himself refers to an internal conflict where a protagonist is struggling with his or her own character, past, or "personal demons." This is also absent from The Swiss Family Robinson, which has a cheerful, matter-of-fact, and unreflective tone. The characters are static, not dynamic, which means they do not change their personality or character throughout the story (except for acquiring new skills). Nor is any personal flaw in them the source of their troubles, which are external.
Man against machine obviously does not apply, as the story takes place in a very low-tech setting.
Nor is the story about Man against God or fate. Though some people might respond a to a survival situation with anger against Fate, or God, for stranding them there, the Robinsons do not. In fact, praying to God and relying on Him to help them survive is one of their major survival strategies.
The story is basically Man against Nature. It chronicles the challenges the Robinson family face being marooned on a desert island and shows their resourceful solutions to the problems of how to survive the storm, get themselves and their animals to the island, use the tools they have, and find food and shelter for themselves for the long term.
The family survives thanks to the environmental knowledge, calm leadership, and resourcefulness of the father, as well as the cheerful hard work of all the other members of the family. However, it cannot be denied that they also survive because of a large measure of luck or blessing. They come well-equipped with tools and livestock, and find an island equipped with many, many natural resources.