The reason why a little of the water the pasta was cooked in is added into the sauce before serving is because the starchy water the pasta was cooked in, helps to create a creamy and silky sauce, by emulsifying the oil and the water components.
The starch in the water acts as a natural thickener and binder and helps the sauce cling to the pasta instead of being watery or slick.
The starch also helps to marry the sauce with the pasta, ensuring much better adhesion of the sauce and distribution of flavor.
When cooking pasta you should not add oil to the water.
Adding oil to the water when cooking pasta is unnecessary for preventing the pasta sticking and also wastes the oil.
Adding oil to the water when cooking pasta also prevents the pasta sauce from adhering to the pasta like it should.
Instead you should stir the pasta immediately after you add the pasta to the boiling water and then stir the pasta occasionally after the pasta is added to the boiling water, which will prevent the pasta from sticking together.
The oil will create a slick surface on the pasta and cause the sauce to slide off the pasta which makes it a bad choice for cooking pasta.
The oil basically forms a film on the pasta and does not mix with the water and won't prevent the pasta from sticking or clumping up.
And the oil also creates an oily layer on the pasta, which makes it less desirable.
To prevent pasta from sticking when cooking pasta, use a large pot, with enough water that gives the pasta enough room to move around.
You should also add salt to the boiling water, which is essential for flavoring the pasta from the inside out.
Once you add the pasta to the boiling water you should stir the pasta immediately and then continue to stir the pasta occasionally as the pasta cooks to ensure that the pasta remains separate.