1. I don't want to include JS from a third party. I don't even use Google Analytics. It's a potential security issue and it's slow.
2. I'm EU citizen, my business is in Germany and I don't want to store customer information on servers in the United States, because the privacy laws are different.
3. Customers might send me sensitive information that I don't want to have on any other system than the ones I own/rent.
4. I don't want to "leak" business internals to a third party. That's why I don't use Evernote, Basecamp or anything cloud-based where any information about me, my company, my revenue, my metrics or my customers is potentially accessible by a (rogue) employee of that service or where any of that information might leak to the public if the service get's hacked - which seems to be not that unlikely.
Some might argue that business-wise I'm at a disadvantage, because I don't use all these fancy tools for A/B testing, metrics, customer support and whatnot, but then the decision for me is always very easy: Can I self-host this software? No? Okay, don't bother with it.
Users asking for help will send you all kinds of potentially sensitive stuff, even if you don't ask for it. Screenshots, passwords, etc. You may not want that in the hands of a third party.