Why are the Great Lakes not considered a sea?
"Sea" versus "lake" versus "just part of the ocean" is a bit fuzzy, but there are two things that are universal about seas:


They are saline.
They are either endorheic or have a sea-level (tidally-influenced) connection to the ocean.


Now, let's see how the Great Lakes look under these criteria.


Saline?  No, salinity is 0, give or take measurement error.  Even the Baltic Sea, the least-salty of the generally-recognized seas, is far more saline, at 0.5%.
Endorheic?  No, they're connected to the ocean by way of the Saint Lawrence River, and have been for at least 10,000 years.
Sea-level connection?  No, the Saint Lawrence River has about 500 km of non-tidal flow below the outlet of Lake Ontario, over which it descends 75 meters.


Score: 0 out of 3.  Not surprising that the Great Lakes are considered lakes, not seas.