There is but ONE truly compelling reason why someone wouldn't want their console to ever touch the internet and that would be piracy.
Nope, there's LOTS of reasons not to like that aspect of it, and for the record I don't pirate my games.
Let's Start with PRIVACY. There's a Camera + Microphone in your home that can not be physically disconnected and have the system still work, then you have an "always online requirement" and the fact that your system will always be on (even when it's "off") so it can "autopatch all your games". Now let's just say you trust MS / the NSA etc... to NOT spy on you... that's one hell of a target for hackers to shoot for. Lots of people hjave issues with that.
Another one that's my "poison pill" is RETRO GAMING. I routinely play 15-20-30 year old games (Combat on the 2600 never get old) and at some point anyone with a brain knows those authentication servers will be shut down or re-purposed. It could be 5,10,15 years down the road but it'll happen and an entire generation of games are now unplayable. If I can't take a game and put it into an offline system, then I simply am not interested and won't spend any money on it.
I may very well be in the minority here, but this is why the XBone will be the first X-Box I don't buy.