Complete control and flexibility.
Do whatever you want with your website. Hack the code, upload files to your web space, rearrange folders, and make your installation as flexible as you want. Since WordPress is open source, there are thousands of themes created for it. Some can drastically alter the appearance of your website.
Maximum extensions via plugins.
Thousands of plugins available to extend your website. Add a shopping cart, or membership option. Realize your dreams with WordPress + some plugins.
Follow your own policies. With the exception of your hosting provider’s rules.
Requires more time and work to maintain.
You have to do the updating & maintenance. If something goes wrong, no company or service is going to do it for you for free. You’ll need to take time out of your day. And due to human error and/or laziness to update, this leads into…
Greater security risk.
Malware (malicious software) targets self-hosted websites because it has potentially the lowest security.
Services that are hosted by a company are often offered at a flat-rate, unless there’s a bandwidth or traffic limit. As your website traffic grows, so does your expenses.