I remember adults saying to me when I was a kid "We could do without your attitude" when they did not like my behavior. It means that things would be going much better without whatever it is that you "can do without". It can be a kind of inadvertent, polite way of correcting someone's behavior since you are not directly referring to the person. Hence, its use by parents and teachers.

Hi, it's not so much "unlucky" as it is an added responsibility or burden that you wish you didn't have. For example, let's say that you want to buy a sports car that just became available, but you are still paying monthly loan payments on an existing car, and you can't afford to pay both installment loans at the same time. You could say: "I could really do without my car payments. That extra $500 a month is just what I need to be able to afford the payments on that new sports car!