Why won't my Shopify store connect to my PayPal account?

Are you trying to connect a personal PayPal account?
If so, you will need to upgrade your account to a PayPal Business account.

When you set up your Shopify account, a PayPal Express Checkout account is automatically created using the same email address used when signing up to Shopify. My suggestion would be that you integrate this PayPal account with your Shopify store.