Considering both metalworking and the Archimedes principle were known since Antiquity?
Part of ship construction involves laying the keel of a ship, and attaching ribs to the keel, then adding the planks to the ribs to build the sides of the ship.
Metal ships didn't really become possible until you could forge a keel long enough and strong enough to resist the bending and twisting of a ship's hull.
Keels need to bend without breaking, but not stay bent. Until we had large industrial foundries, the biggest item you might find that was like that would be a sword, or a spring. Imagine the forge it might take to make a sword 100 feet long, and you see why metal ships weren't really possible.
Now, Metal cladding has been used on ships since antiquity, in rams and armor. But that's not the whole ship, because for that, wood was better; it already grows in convenient 100-foot-plus lengths, bends and shapes easily, and can be quickly formed into a curved keel by a small group of men.
Metalworking may have been known since antiquity but a ship is a huge amount of metal. Ships weren't made out of metal until the 19th century for the same reason that buildings, bridges, vehicles, and furniture weren't made out of metal: it just wasn't available in sufficient quantity and was just too expensive.
Prior to the 19th century iron smelting was done in bloomery furnaces. In this process you combine high-grade iron ore along with charcoal in a chimney with pipes for ventilation at the bottom. Control of the fuel and introduction of air through bellows enables the fire to reach a temperature of about 1,000 deg. C while combustion of the charcoal produces carbon monoxide (CO). The CO reduces the iron ore, producing pure Iron. The heat of the fire keeps the Iron hot, but not molten, which is critical for this process. The Iron is merely hot enough to weld, which it naturally does, creating a sponge of Iron metal welded together while impurities such as glass and slag will be molten. When the spongey bloom is pulled from the fire it is hit with hammers while still hot, which forces out the molten impurities, leaving behind a solid and relatively pure chunk of Iron.
However, this is a relatively labor intensive and low volume process. It also relies on higher quality ores being used, generally. As a consequence of this the volume of production of steel was generally quite low compared to modern standards in pre-industrial times. Even with continual operation of lots of bloomery furnaces by lots of workers production is limited to only a few kg per bloomery per day.
Starting in the late middle ages several innovations occurred in production of Iron/steel beginning with the blast furnace. Generally, mass production is facilitated by handling molten metals, however making high quality steels with a molten process is problematic because it's tricky to get the composition right. The advent of the blast furnace made low grade steel (pig iron) available in large quantities but it took quite some time before it was possible to produce high quality steel from pig iron. In the late 18th century the techniques of making crucible steel were worked out and in the 1850s the Bessemer Process was invented. These processes use molten steel and produce high quality, strong steels in enormous quantities. By 1800 the production of steel by England alone had reached into the thousands of tonnes a year, by the 1870s production would be 2000 times greater, leading to the massive boom in use of steel for manufactured goods and construction.
Look at some simple figures for metal ships. In 1861 you have the USS Monitor, at about 1,000 tonnes, a relatively small ship at the time. Yet it used nearly as much steel as was produced in a year from a major country like England in 1800. It was only with the massive increase in steel production of the 19th century that sufficient quantities of metal became available for use in ship building. Consider a larger ship, such as the USS Oregon (BB-3), a battleship built in 1893 with a displacement of 10,000 tonnes. It would simply not have been feasible for any country on Earth to build a ship using so much metal prior to the 19th century. Compare that to the HMS Victory, built in 1759, Lord Nelson's flagship, with a displacement of 3500 tonnes and built out of wood.
And that's aside from the general lack of tools and techniques for metalworking on a large scale prior to the 19th century. In 1700 welding metals was a thing that you did by putting small work pieces into a fire and heating them up to welding temperature before beating them together with a hammer and anvil. In 1900 welding was a process using various specialty tools (electric powered arc welders, oxy-fuel welders, or thermite) on large pieces of metal in situ.
As others allude to it was for primarily economic and engineering purposes. It took an Industrial Revolution to create the ability to make that amount of iron cheaply enough as well as iron forging and engineering techniques sufficiently advanced to create a reliable safe vessel.
Once this occurred it became cheaper to make metal boats than wooden ones. In wood every piece must be created out of a piece of tree that isnt a boat. With iron you can fairly cheaply create complex structures.
That much iron would have been extremely expensive.
Before the advent of steam engines, a ship that heavy would have been extremely difficult to move.
It probably wasn't necessary in the 18th century. A wooden hull multiple feet thick was far more effective against cannon balls then most people give credit. As cannons improved the need for stronger hulls did as well.