Why does it happen? Cloudflare works as a proxy, taking HTML from your server and returning it to a user in optimized form. Because all requests go through their servers - there's one additional hop. With this hop TTFB increases significantly.
Although I agree that TTFB is actually not that important from end user's perspective, the reason why Cloudflare wrote this article is strictly marketing.
For more information, see a long comment I wrote on this a while back (note: while reading, remember that a CDN typically has a server very near the end user but not so near as to be on the other end of the last mile of their network connectivity; in essence, they are a reverse proxy solution positioned in the network where a forward proxy would normally go), as well as the response someone left: