I think there's a lot of reasons.
From an industry standpoint, I definitely think a huge reason is that Nintendo is not standard. As the industry has shifted focus from the East to the West over the last 10 years, there's very much been a standard recipe that has evolved if you want to succeed. You take a large team, give them copious amounts of money, get them to make something graphically stunning with guns and/or violence, then you market it to males aged 16-35, and then you wait for the money to roll in. Obviously that doesn't cover everything, but it's become more and more the way things are done.
Nintendo doesn't do any of that. So there's this idea that they are an outsider. And in an industry where things are becoming more and more standardised, the concept of there being an outsider who not only does their own thing, but also is generally very successful at doing it. And that's a thing that scares anyone in any industry. If everything is standard, it's much easier to out spend or out market someone. When you've got an unpredictable actor in the market, it's worrying for those who have all their competitive advantage in being able to out spend or out market, because those things are less important. Nintendo going third party would force them to standardise, and that makes it much easier to compete against them.
From a gamer/media standpoint, I think it's a mix of things. There's no doubt that there's a 'I want Nintendo games but don't want to have to buy their hardware' viewpoint, and that's totally valid. But there's also (and this is mainly media based) a 'This company doesn't put forward the image of gaming that I think is best', which really at the core of it boils down to a 'I don't like kiddy games' argument.
What I find stranger than people continually predicting that Nintendo is going third party/out of business/whatever, is this underlying desire in people that they want it to happen. I think that's really strange. Nintendo is a gaming company. It relies entirely on the industry for its survival and prosperity. It is in the best interest of Nintendo for their to be a large, thriving marketplace of consumers who all love video games. I know there's a big desire for the industry to 'mature' and been seen as legitimate, but I just find it so strange that developers/publishers have been so quick to sell themselves to Microsoft, who have specifically stated that their entire goal of entering the industry it to trojan horse their ways into the living room so they can sell their OS and related services. They'll flick video games aside as soon as they can make that happen.
I think if you asked film makers if they'd like to go back to the time when every studio wasn't owned by a media conglomerate, they'd say yes in a heart beat. But the video game industry seems like it wants that to happen as fast as possible, and they're willing to lose the actual video game companies along the way to make it happen. It's weird.
