One, a forgotten semicolon or a missing quote mark can take down the whole site, and you can’t get back to the editor to correct the mistake. You can get in over FTP, but many people don’t really realize that since many have never used it. A lot of hosts have installers that install WordPress so everything happens behind the scenes. Browse these forums. There are quite a few threads just like that.
Two, if you use the editor you are essentially working without a backup. The built in editor encourages that. It is possible to break something and not know about it for hours or days. Backtracking is very difficult at that point. Even if you know about FTP by the time you login you may have forgotten what you did.
It is really the same logic as for not working on a live site but one step worse. With that editor, not only are you working on a live site but you are working on a live site using tools that are dependent upon that same live site.