Welcome to the PayPal community! I'm sorry to learn that you want to close your PayPal account and you are facing issues with logging into your PayPal account as you don't have a phone number. We value you as a customer, and we ask that you carefully consider your decision. If there's a chance that you might want to use PayPal in the future, it's a good idea to keep your account open. There's no fee to keep your account open.
There is no easy way of saying this, however, login issues are sensitive, and to fix this you will need to get in touch with us over the phone. It involves verbal verification related to the information on your PayPal account. Once you are able to login you should be able to proceed further. Here's how you close your PayPal account.
I'd recommend reaching out to our Customer Support teams by clicking "Contact" at the bottom of any PayPal page for further assistance.