There are advantages of self hosting as Baloo mentioned, the disadvantages and contextual advantages of remote hosting might be:

• Persistent physical location
• Electricity backup needed
• Data backup to be effective
• Very good and cheap internet connection, many providers don't let high upload bandwidth.when you ask for it, they say bring your server to our data center and putting in front of you many logical causes. All seemed correct and that's why there are data centers.
• Data security of the professional data centers is needed
• The flexibility of a vhost is a big comfort. If you have a video broadcast event increase the CPU power 10 times on these hours and then return to average.
• S3 may give a big storage possiblity with 0,002-0.006usd  per GB, 
• No worries about hardware failures in vhosts they always work. 
• No worries about natural disasters. There is even a chance for a lightning strike to affect/destroy the self hosted server.

But if I had all the needed parameters of a good hosting environment in house, yes I would also prefer it to feel independent :)

Agree 100% with Baloo and Cem 

I would add to what Cem wrote that sleeping at night is a part of good meditation session. Hence if you are a yogi consider that because if you host your own site, there will be sleepless nights when something crashes and you have to troubleshoot through the night.

Ask yourself this question:

Why dont I be my own phone provider?

It is possible to do it! Yeah! But why not? May be the answer to that is the same solution to hosting your own site. 

Andrew mentioned something about knowing what you are doing. No Shit!