Having your own web server is more expensive than the cheap web hosting options. But here is the Benefits why would you choose to run your own web server:

• What happens if one of the websites get hacked on the shared server? This probably wont be your fault but all it takes is one site to be exposed and the entire web server can be hacked and yes your site too. So, better option is to host your own server.
• How your custom email goes into peoples junk mail folders? This will be because your web server is blacklisted. You can solve it easily if you have own server.
• It offers a good learning to understand server setup and configuration.
• You have full control, you know every bit of hardware and software that has gone into it.
• When you need to reset the server or install anything you don’t need to contact tech support and wait for a response, you can simply pull the plug yourself.
• You will never get hacked because of another persons insecure website running on the same server.
• You can use every bit of your hardware resources that will help in smooth running of your website.
• It's a great way to learn and adapt new technologies day by day
• You can secure almost everything if you have own server. Hosting servers are just another computer that can be accessed by anyone. So, you are safe here if you have own server.

What are the drawback of running own web server:

• If something goes wrong, you are the only person who can put it right. All security updates need to be done by you.
• When you temporarily loose your internet connection or power your website will be offline.
• Your internet connection speed may not be fast enough for the number of viewers.
• Your ISP (Internet Service Provider) may not allow you to host a public web site on your home network.
• Some computers may not provide an economical alternative in terms of power consumption vs. external hosting fees.
• If you have high end server then you need a cooling space too. Like you have to run AC 24 hour to maintain server room Temperature.

Hope this helps :>