TL;DR: Multiple factors conspired to make big sailing ships impractical.
There is a multitude of factors that, put together, caused the American cultures not to develop significant seafaring capability. If I were to point out the most important ones, they would be:
- Lack of exploitable sea routes
- Lack of metal tools
- No large-scale cultural interchange
Lack of exploitable sea routes
The development of seafaring capabilities in Eurasia occurred primarily in two locales: The mediterranean, and later the North Atlantic area (with the North Sea, Baltic sea, etc.). Why this happened had a lot to do with what there was to gain; after a bunch of civilisations sprung up in the fertile crescent, north Africa and Greece, there was a lot of money to be made by trade. There was also the silk road, spice trade with the Indies, and the Norse of course loved to go viking for fun and profit.
Now, technological development happens on the margins. If you can make a small improvement that impacts your bottom-line, you will take it; if it requires a significant investment with an uncertain result, you probably won't. This means that technological development is more likely to happen by increments, and if you take a look at the development of ships in Europe; from rafts and rowboats, to lateen-sailed ships, to Viking drakars, to caracks and galeons, you'll see that it is very gradual.
Basically, someone figured out they can make more by transporting the goods for cheaper and more quickly by water than overland, and started shipping them; from there, a sequence of small improvements resulted in the current state of technology.
In America, there was little reason to do anything like that; the big empires were all inland, and the cultures living on the islands of the Carribean mostly just lived on subsistence agriculture, and didn't have anything for sale that you couldn't just as easily grow or make on the mainland.
Lack of metal tools
You don't need metal to make a seaworthy ship, but it helps a lot. Iron nails and tools alone make shipbuilding a lot easier. This doesn't mean it's impossible to build a ship without them, but it does make it more work-intensive and therefore expensive, so anyone is less likely to actually invest in the endeavour (see above) and thus to discover that establishing sea routes can really pay off.
No large-scale cultural interchange
Eurasia and Africa put together are huge. Remember what I wrote above about progress being a sequence of small improvements; any small improvements that helps somebody's bottom line is highly likely to spread as soon as it's seen in use. This means that the successive steps tend to happen more quickly (since there's more people looking at the same issue), and thus the overall development is sped up.
In comparison, the American empires were mostly isolated; certainly the trade routes didn't extend over such a humongous area and huge population, which again also contributed to relative lack of trade opportunities.