Being rich means being able to provide one’s basic needs and still have enough to keep as back up. It also means having more assets than liabilities.
Having more assets than liabilities just means you have a positive net worth, it doesn't mean you're rich. If you've got $1,000,000 in cash and $999,999,999 in liabilities, your net worth is the same as a guy who has $1 and no liabilities. Neither of these people is rich.