1) When your economic situation goes south… and I know that nobody ever expects it will, but these things are inevitable. Not for everyone per se, but yes, there will be snow in the winter and financial struggles between couples. If and when you get into financial trouble, with separate accounts, you may be able to preserve one mate’s credit score.
2) Further, upon a messy split or even worse, a death, your spouse’s liabilities become yours on joint accounts and supplemental cards. So, if he runs up $10,000 in charges for seasons tickets to all of his favorite teams… you may be on the hook to foot the bill.
If you ended up with a supplemental card but did not actually sign the credit card application then you can easily remove your name from the account. However, if you made a joint application you should either write a letter to the credit card company ‘blocking’ one of you from using the card going forward, or you should cancel the card and start anew with separate accounts.