For one, using services like Gmail and Hotmail means giving governments access to your data. And then there is all the stuff a provider can do to your data. They may cancel their service or cease to exist like MegaUpload. Providers could modify you data. mc.fly gives the example of a video he made about the new data retention in Germany. It only used CC-licensed music. Nevertheless, the audiotrack was removed on Youtube because of copyright violations.
Service providers steal your data. There is the famous example of Instagram changing their ToS to All Your Images Are Belong to Us. They did change that policy quickly after it was announced under the weight of the ensuing media shit storm. Providers are vulnerable to hacks to substantiate his claim mc.fly simply presents a list: Sony: how often? GoDaddy Dropbox AT&T Valve Living Social and so on and so forth
After giving a list of arguments as to why to f*cking DIY mc.fly says that these arguments can basically be summarized these days with a single image.
So. Run your own shit! You don’t need to do it alone. You can go to your hackerspace and collaborate.