Because of the Commissioners' Plan in 1811. Up until then, Manhattan above Houston Street was mostly farmland, or else uncultivated land owned by the city. The city's population began booming in the post-Revolution era, so both the city and the owners of the large uptown farms/estates were interested in parceling off their land for real estate development, as the downtown area that made up the entirety of the city began to get crowded.
The Commissioners' Plan of 1811 surveyed Manhattan, and established a grid by which the city would be laid out. The plan was approved, and construction of paths through these estates was begun.
For example, one of these estates was owned by Clement Clarke Moore, author of Twas the Night Before Christmas. His estate was on the west side of the island and called Chelsea, and his original landholding is just about where the current Manhattan neighborhood of Chelsea is today. With the help of a real estate developer, he began to sell off parcels of Chelsea in the 1820s, just as soon as 9th Avenue was laid out.
Nothing like this ever happened in Boston, so Boston is a collection of streets much more like Manhattan is south of Houston Street.