Nintendo strongly shows outside as one developer even though they have several dev teams. Sony does not, and MS does not. They have teams with well-known names even to the public. That alone is a huge thing. And then there's the fact that Nintendo has managed to associate its name with quality, which lessens the need to differentiate different IPs or games by different studios. Sony and MS's 1st party titles on the other hand vary more in quality, or at least that's how it's perceived.

Simply because most gamers when they think of Nintendo think of first party , the two go hand in glove it's why you see all those lines written about Nintendo , regarding first party versus third party impact.

I believe they were speaking out of spite for the company, and not the games themselves.

I've seen it plenty of times :p Of course, people usually make that generalization to enforce their own biases, rather than actually disliking a common theme about them.

Like i said though, generalizations can have exceptions. They can also encompass multiple unconditional perimeters (such as both "cartoony" games and "ones without a story", even if there are some examples that only fit one, the generalization still fits). For the sake of simplifying conversations, they're useful.

I saw someone the other day claim they always hated voice acting.

Because they all share a standard of quality and excellence.

Nintendo has a familly friendly approach to Nintendo games. Nintendo tend to make games that can be played by a broad range of players. This is especially true when in come to difficulty and teach you the game. Nintendo game will all start has if you never played video game before and appeal to every gamer.

Some gamers that are fans of a genre and expect a challenging game, will feel very annoyed with having to play the tutorial mode in every Nintendo games.

Not liking Nintendo games is saying that you don't enjoy the casual game experience and all inclusive approach of Nintendo.

1st party games.
Usually mascot-games.
Usually platformers.

Perhaps it's just me, but I find it pretty easy to justify the term "Nintendo games." To me, they provide a pretty similar experience, or at least a pretty similar role.

If video games could be compared to food, then I'd consider Nintendo games a dessert. In general, short, sweet, and not particularly nutritious, but easy to enjoy and enjoyed by a lot of people.

With that said, I don't see anything wrong with someone saying they don't like dessert.

But that's kind of the point, Nintendo games consist of many different genres and many of them are vastly different.

Mario platformers, Mario Kart, Smash Bros, Fire Emblem, Advance Wars, Pokemon, Xenoblade, Zelda, Metroid, Kirby, Yoshi, Donkey Kong, Kid Icarus, Pikmin, etc. 

Most of these games aren't really comparable to one another so that's why it's hard to block them all together as one general type of game.

It's not about the differences it's more to do with how Nintendo first party is equated to Nintendo the company ,  and human nature being what it is this gets filtered down to the Mascot type games that people grew up  being seen as "Nintendo" similar to how Anime is associated with large eyed characters stemming from Tezuka , even though in reality it has much more variety in character looks , just remember perception and reality don't allways coincide.