Here is her reasoning;
Her $14,000 is equity in the business. Your $6,000, if the business is making the payments is not equity but debt. If the business is paying the credit card bill, then it's almost like you did not contribute anything except. In reality, you are bearing the risk that the business fails and is unable to repay the loan in which case, the loan becomes your responsibility.
Let me illustrate with an example. Let's say you earn $1,000 monthly, and you have expenses of $200, profits would be $800. If the credit card payments are $100 and the business pays, profits go down to $700.
WHat should happen is you should take your share of the profits, let's say 50% ($400) and pay your credit card debt. That's the only way to be fair to your partner.
Between where you are and where you want to be, there is always a way