Not all unemployed people receive unemployment benefits from the state. I get the impression that you are unemployed and not receiving any such benefits. In other words, you have no income whatsoever, neither earned nor other than earned. So, for you chap 13 would not likely be available because you lack the means to pay anything on your debts, no matter how they were reorganized. That's what the article is saying. It is saying that, for you, only chap 7 would be an option.
Having a source of income helps a person qualify for chap 13. That doesn't matter to you, because you are not trying to get chap 13. You have no reason to want chap 13. You want chap 7. It simply is not true that a person needs an income to file chap 7. In fact, not having an income is an advantage.
The main point of the article is that you need an income too small to pay your debts in order to qualify for chap 7. Well, "no income" is certainly too small.
It is illegal to borrow money with no intention of paying it back. That's called "fraud." So, if you ran up credit card debt when you had no income, that might raise a legal concern. The bank might alledge that you knew you would be unable to repay the debt at the time you were charging purchases. Your attorney might be concerned about protecting you from that accusation. That's the only way I could see your attorney wanting you to first get a job and make some payments. But you have to ask what is the likelihood that any bank is going to accuse you of fraud? That is hard for a bank to prove. It is not illegal for unemployed persons to use credit cards, as long as they have some hope of eventually having an income.
If you went out and ran up a bunch of credit card debt, knowing good and well that you would probably never pay it back, then your attorney might have a point in discouraging you from filing bankruptcy. If that's not what happened, then you have as much a right to file for chap 7 bankcruptcy as anyone else.
People with absolutely no income file for chap 7 all the time. Suppose a person with a lot of debts gets permanently disabled and cannot work. What do you think that person is allowed to do?
Also, keep in mind, you have the option of simply defaulting on your debt. (Just not paying it.) Perhaps you're already doing that. Unless you are guilty of fraud, there's not much your creditors can do to you.
I'm wondering what exactly is your lawyer wanting you to do? Maybe your lawyer just doesn't want to bother doing the work of filing for you and figures you just ought to default. The consequences 10 years from now are about the same, whether you file bankruptcy or just default. In 10 years, those same banks will offer you new credit cards.