The internet, with all of its amazing benefits, is still not secure. While you may connect with HTTPS (SSL) and you think your traffic is encrypted, is it really? The person who owns your server can decrypt that traffic, which would show your user agent, IP address, etc. Not to mention the sites that may just start downloading files onto your computer, or host other malicious files that could harm your computer.
The internet is constantly expanding, and we can’t know for sure what sites are safe and what ones aren’t. Truthfully, the internet really isn’t safe for anyone, no matter how much you think it is.