The distinction you're making between employment insurance and welfare is misleading and propagates a misconception that some government benefits are entitlements.
How are you defining welfare? What Canadian programs do you consider to be welfare? There's a good discourse on the rise of "workfare" state programs and the transformation of welfare programs; maybe this is what you are referring to? If this is the reading you're taking (anti-liberal) then you probably have some basis to say EI is not welfare, at least by the standards of the last half-century.
In most countries, welfare refers to the application of government programs to ensure basic needs are met during difficult times. EI is one of these programs, providing financial assistance during periods of unemployment, parental leave, illness, or to care for someone else.
To suggest EI is not welfare because you pay a premium is disregarding the fact that the program is completely administered by the government for the welfare of Canadian residents. Sure there are are conditions and requirements that need to be met to qualify for these programs (work so many hours, pay certain amount in premiums, lose some income, etc), but EI is a welfare program by its design.