Why is the first section of Gulliver's Travels often considered suitable for children and not the others?
One reason that the first part of Gulliver's Travels is considered to be more suitable for children has to do with the subject matter. In the voyage to Lilliput, Gulliver is surrounded by thousands of tiny people, but he is never really in any danger because he is so big in comparison. There are lots of comedic situations in this part, or, at least, many events that could be adapted as entertainment for kids. In the voyage to Brobdingnag, Gulliver is the tiny one, surrounded by a community of giants. He finds himself in mortal danger more than once, and this is demonstrably less funny than his experiences in Lilliput. Also, because Gulliver is so small, things like the giants' skin and flying insects look absolutely disgusting to him, and this seems less suitable for children, as do the multiple sexual situations in this section. The third voyage has a lot to do with complex science and pseudoscience (some of it pretty gross), as well as geometry, Gulliver has to abase himself to a ruler who routinely kills people by poisoning the floor he forces them to lick, and the inhabitants of a floating island use their privilege to force those who live underneath them into submission by threatening to bring the island down on top of their heads. Not kid-friendly stuff. Finally, the fourth voyage presents a group the natives call "Yahoos": they are humanoid creatures who poop on Gulliver from atop trees, who run around naked, are covered with an unusual amount of body hair, and kill each other for shiny things—probably not good behavior to show to children. In other words, then, the first part is most easily adaptable in subject matter and because it already relies on humor to a large extent.
Further, there are two types of satire: Horatian and Juvenalian. Horatian satire tends to poke fun of something in more indulgent terms, while Juvenalian satire is a great deal more biting and caustic in nature. The first part of Gulliver's Travels is Horatian, and the remainder of the text is either certainly Juvenalian, or, at least, a mix of the two. For example, the Brobdingnagian king denounces humanity in the most critical terms as do the Houyhnhnms of Houyhnhmnland in part four. It would be tough to soften this for children's entertainment.
The first section of Gulliver's Travels deals with his experiences on the islands of Lilliput and Blefuscu, where the people are tiny. The fantastic nature of these stories, plus the generally harmless political satire, make them appropriate for children. The later sections of the book have fewer fantasy-adventures and more overt satire, most of which is too obscure for children to understand. Additionally, the classic 1939 Max Fleischer animated film only adapted this first part, eliminating much of the satire and adding a romantic fairy-tale subplot; many adaptations, including the most recent live-action film, followed this lead. Gulliver's experiences on Lilliput were the most innocent of his travels, and people who haven't read the book are often unaware that there are any further parts to the story.