Aside from the fact that the author of the blog doesn't really provide any "reasons" in their blog ...
There are ZERO reasons not to use your own domain name for email.
The biggest reason TO use your own domain name is that you are not subject to the corporate whims of your ISP, cloud-email provider or whatever. You get to choose, and you get to choose when to switch.
The only thing you should NOT do is attempt to host your own email server on a home internet connection. Not only do most home ISPs (quite rightly, IMHO) block port 25, but also most home ISP IP ranges are on blocklists.
To make it clear: Nothing wrong with running your on mailserver. Just don't do it on a home internet connection and then bitch and moan about how its not working !