When you close a credit card account, you lose the value of that card’s credit limit in the credit usage calculation. The credit limit is an important component when determining a consumer’s balance to credit limit or the “credit usage” ratio. This ratio rewards consumers who have low credit card balances relative to their credit limits.
If you close credit cards, especially those with large credit limits, you will likely cause your credit usage ratio to go up (if you carry balances). This can cause your score to go down considerably.
Additionally, if you close credit card accounts the credit bureaus will eventually remove them from your credit reports. Even though it can take years for an account to be removed from your credit reports, once it is gone you will get no credit for your responsible management of that account.