Product: Credit card or prepaid card

we received a bill with an annual fee charge on it from Chase. It was a southwest airline card. We had not received anything from them until XX/XX/XXXX. My wife thought it was her card because she closed hers earlier this year, and thought it was a mistake or that they had lowered the annual fee instead of closed the account. But we later realized that it had my name on the bill and I could n't recall even having this card with them and called to close the account. I found out from their automated system that I had not used this card since XX/XX/XXXX So why am I now just now getting a bill with a annual fee? this question I asked XXXX XXXX who in turn told me that they had change the policy for this account and that even if I closed the account I would still be charged the annual fee.even if they closed it, I asked how is that and I was told because it was over thirty days before calling to close the account. I said to XXXX XXXX in Ohio, why were we not notified? he said that you were, it was written inside the bill, so you will still be charged. I said so get me someone on the phone that can waive this fee and closed the account. He told me specifically twice that there was no one else for me to talk to but he would close the account and I would need to still pay the fee. I said no sir, I will pay you one month of the fee but not the entire thing and I want the account closed. He told me no and that I would have to pay the fee regardless. I said a second time that I wanted the entire fee waived and account closed or I wanted to pay the one month and the rest credited to my account. He still refused. I said to him that I will then pay it, but place a complaint with the CFPB and in the mean time I wanted it put in writing and sent to my email what he just told me and also tell me where it was written in my bill. ( by that time my wife had read the bill and it was not a written notification about the annual fee but it did have in there a paragraph in regards to how the annual fee is charge./ But I had n't had a annual fee charge to me again in almost 5 years. ) he then said that he would need to transfer the call to someone that could help me better about the fee, I said but wait XXXX I thought there was no one else that could help me. He said I am transferring you to someone that could help please hold the line. Then he and an XXXX came on after about 5 minutes and he said that that he told her about me wanting to file a complaint with the Better Business Bureau, I said no sir the CFPB and then XXXX took over the call. She did very reluctantly say that she would waive the fee and close the account. and that It wills how in 5-10 days. 
I think that Chase has gotten to be really ridiculous with their tactics. They are bully 's and I believe that this is underhandedness on their part and uncalled for. A mere {$40.00} could not be that detrimental that they have to pull this. Normally creditor close your account after 2 years on inactivity especially Chase as we have had other accounts with them. I think this is pretty low and if I did n't know that I had the CFPB as a recourse or knew my rights I would have had to pay them any way. this is terrible action on their part/