It is a historical convention that goes back to definitions: ships carry boats. Since early submersibles could be carried by ships, and were often tended by ships called "submarine tenders", they were boats, and the naming convention held.
The earliest modern submarines, dating to about 1912, were much smaller than those used in WWII and later, and were often carried by ships to a place near their objective because they typically lacked the fuel needed to make long return trips.
The first practical submarines were developed in the 19th century as small vessels for 1-4 crew that were typically transported aboard larger vessels and deployed from them. Even when submarines became large enough to be considered more ship than boat, there remained a self-deprecating pride among the crews to continue using the diminutive term. The German term for a submarine is unterseeboot which became anglicized to U-Boat, a term that was popularized in WW1 and WW2.
Submarines are very much considered ships however the earliest submarines to enter naval service were formally titled Submarine Torpedo Boats. Submarine Torpedo Boat was rapidly shortened to Submarine officially but the monicker "Boat" stuck as an informal type name and submarines have been known as boats ever since. The Navy's official designation is Ship, Submersible, Nuclear for fast attack subs, and Ship, Submersible, Nuclear, Ballistic for the ballistic missile launching subs.
By the time submarines had grown into ships, the tradition of calling them "boats" had been established and has remained until today, at least to some extent. Make no mistake, a vessel that is 377 feet long and displaces 8700 tons is indeed a ship, regardless of tradition.