Well, for some reason you think https://example.com/ will set some cookies for you, and not, for example, an image embedded inside html returned by https://example.com/ or javascript embedded inside or css embedded inside or one or more combinations of both

Also, could be https://example.com/ doesn't like the headers you're sending, so it doesn't give you a cookie

Also, it could be a proxy of some sort between you and https://example.com/ interfering

Also, it could be some firewall or antivirus or somesuch interfering on your machine (or on proxy between you and https://example.com/ )

Also, it could be anything :)