I think my answer would be a long one, unfortunately, because access to EI can be a complicated subject.
Some people aren't eligible for a number of reasons. One of those reasons is that a number of those people do not contribute to the program. Nearly 30% of unemployed workers don't contribute to employment insurance. In that case, they aren't eligible for benefits. Another 16% aren't eligible because of their job separation. It might have been a voluntary leaving or something like that.