I seriously doubt there is any way to reopen your closed Chase credit cards since Chase has decided you are a credit risk. But you can certainly call Chase to argue, hopefully after receiving their reasons in writing.
I would also get a copy of your credit report and see if there are any errors to correct. Check how many credit inquiries you have on each credit bureau. You'll want to take a break from credit card applications and focus on improving your credit. Accounts closed by the bank can hurt your credit, so I would argue to have the closure listed as "closed by consumer" on your credit report if at all possible.
It sounds like you did not wait 90 days between credit applications which is frequently recommended on these boards. Not that that is a reason to close your accounts, but it contributes to your high number of recent credit inquiries.