There are 2 parts to SSL: a) customer-facing, and b) server-side
The customer-facing is optional; whereas the server-side SSL/TLS is required (and already provided by most modern hosting companies).
Read more: SSL Explained - Back and Front
PAYPAL:
You can use PayPal Express Checkout without offering SSL to your customers to protect their data-entry (such as address/email/phone identity info) ... as long as your server is capable of doing modern TLS 1.2 communication to PayPal in the background via CURL for the actual payment handling.
To use PayPal Payments Pro you MUST offer SSL on the customer-facing side because they're entering credit card details directly on your store, and that MUST be encrypted via a properly installed SSL certificate.
But in this modern era where SSL certificates can be obtained for free (ie: LetsEncrypt) there's no good business reason to not offer SSL to protect your customers' shopping experience.