why was the submarine invented?

The Confederate States needed a way to attack blockading Union ships effectively and they were desperate enough to try it.

like many inventions we owe this to the military
Although experimental submarines had been built before, submarine design took off during the 19th century. Submarines were first widely used in World War I, and feature in many large navies. Military usage ranges from attacking enemy ships or submarines, aircraft carrier protection, blockade running, ballistic missile submarines as part of a nuclear strike force, reconnaissance, conventional land attack (for example using a cruise missile), and covert insertion of special forces.

The Turtle was the world's first submarine used in battle. It was invented in Connecticut in 1775 by American Patriot David Bushnell as a means of attaching explosive charges to ships in a harbor.[1] Governor Trumbull recommended the invention to George Washington and although the commander in chief had doubts he provided funds and support for developing and testing the machine.

Leonardo da Vinci (1452-1519) made sketches of a submarine and William Bourne, a British mathematician, drew plans for a submarine in 1578. But it was only in 1620 that Cornelius van Drebbel, a Dutch inventor, managed to build a submarine. He wrapped a wooden rowboat tightly in waterproofed leather and had air tubes with floats to the surface to provide oxygen. Of course, there were no engines yet, so the oars went through the hull at leather gaskets. He took the first trip with 12 oarsmen in the Thames River " staying submerged for 3 hours.

http://www.submarine-history.com/subreviews.htm

why was the submarine invented?

So you could fly underwater