Frankly, because they were one of the largest afloat, with aggressive expansion plans unburdened by extraordinary war debt at first, and with a record of notable victories in recent memory over their local foes in the Chinese navy, and later the Russian fleet.

And with the scuttling of the German High Seas Fleet it left them as the 3rd largest navy in the world behind the British Royal Navy and the US Navy, ahead of the few other remaining dreadnought owner nations like France, Italy, the two side of the Russian Civil War, the crumbling Ottoman Empire, Brazil, Chile or Argentina. And while the IJN had not done much in the war besides cruise around for the German Asiatic squadron, siege Tsingtao, and send a small force to aid convoy escorts and anti sub work in the Mediterranean, the force was very much observing and learning whatever the officers and men could.

And while the Royal Navy had been instrumental as a model, source of professional development, and material support for the IJN, by the early 1920's that relationship was rapidly fraying. Geopolitical differences and points of friction had left the Anglo-Japanese Alliance on its last legs, and shortly to be abandoned completely. In part because of closer Anglo-American ties, feelings or dishonest or unfair dealings at the Paris Conference, and competing Imperial ambitions and interests in East and Southeast Asia.

Japan's industrial base it must be said was far smaller than her seemingly most likely foes, she was not without resources to produce, modern, capable, and well built combatants. A perfect example is theKongo class ships, the first of which was designed by George Thurston of the Vickers company and built at their yard in Barrow-in-Furness before delivery. Her 3 sisters though were all built domestically, including Kirishima and Haruna being awarded to private shipyards vs a naval owned yard, demonstrating again that if not huge that Japanese domestic shipbuilding could at least keep up on a ship for ship basis to a point.

All of this then tied into the force the IJN sought to field, known as the 8-8 Scheme, where 8 modern Battleships would be paired with 8 modern battlecruisers would form the core of the battle line and flying column. While outnumbered by perhaps up to 50%(if everything planned for was actually funded and built in the early 1920's) by their most anticipated foe in the US, the IJN had the advantage of more regional concentration vs the dual coast, and global interests of the US. The IJN actually got pretty close to having the fleet done, they got 10/16 of the initial hulls built even if the time frame meant the oldest were showing their age. The 4 Kongo's, the 2 Fuso's, 2 Ise's, and 2 Nagato's were all completed with a pair of * Tosa* class ships and a quartet of Amagi's to finish the first fleet, with the replacement or maybe even supplemental Kii class battleships being worked on as well while the Treaty was being discussed. Ships then would have been replaced in the first line with newer hulls on a rolling basis to provide secondary forces, reserve vessels, or simply to control costs while remaining potent as needed. They could also build damn good ships, Nagato was arguably the best of the ships afloat in any navy when the treaty was signed, and part of the 'Big 7' those ships armed with 16in guns not scrapped by the treaty.

So as the goal of the Washington Naval Conference was to avert another costly and potentially negatively reinforcing naval arms race, it makes perfect sense to include the third largest fleet. We should also note that Washington produced several other treaties and agreements, which did rankle Japan and other powers to varying degrees but were eventually accepted as well, everything from how the powers would conduct themselves in the Asian mainland, to allowed defense works and fortifications on new Pacific territories was covered. For these topics it made perfect sense to include Imperial Japan as well.