Here's why:
* The statement is clearly sarcastic. Swift is implying that he *does* have a personal interest in promoting this work. He uses words like "sincerity" and "least personal interest" to create a sense of insincerity.
* He plays on the reader's expectations. The typical expectation would be for someone to declare they are acting out of pure altruism. By using this language, Swift subverts those expectations.
The irony allows Swift to be subtly critical of the work he's promoting while still seeming to endorse it. This is a classic satirist technique, which Swift was known for mastering.