As a self employed person, you MUST pay into CPP. You pay both the personal and employer contributions. You do not have to contribute to EI but of course you can not collect it.

CPP payouts at retirement are based on how much you have contributed.

If you manage to claim expenses that bring your income down to the lowest level then you will not owe any tax. It would be rare for this to happen after the first few years unless you are not actually making any money.

So technically what you heard is correct. You can not claim EI if you do not pay into it and your CPP when you retire will be based on your contributions.