A counter to the common anti-Daenerys sentiment
1) "Daenerys is becoming the Mad Queen."
Probably the most common theory about where Daenerys' story is headed. People usually use her punishment of the Masters, the khals, or her single-minded focus on the Iron Throne as evidence of this. And, of course, her parentage.
It's not bad as far as speculation goes, and maybe it'll happen somewhere down the line, but I haven't seen any strong evidence of it in the show. Dany is certainly a very passionate person, and one that takes her idea of justice very seriously, but she hasn't done anything more extreme than we would expect from most people in TWOIAF in her position. The most extreme thing she's done is killed all the Masters, and crucified many of them to boot, but she reevaluated her actions when she was confronted by Hizdahr zo Loraq about his father. She was faced with the idea that she had acted with a heavy hand, and she tried to take a more even keeled approach to doling out justice moving forward. That's not what someone who's insane does. In contrast, Robert never seemed to regret his decision to have all the Targaryen children killed, and even insisted on finishing the job years later when he heard about Daenerys.
Also, as far as the comparisons to her father, it just doesn't fit. Aerys was extremely paranoid of everyone around him. Even the people closest to him were potential enemies. If anything, Dany needs to be a little less trusting of some of the people in her inner circle... such as Daario "Suspicious Motherfucker" Naharis.
Viserys is another comparison that's often made, but I also don't see that fitting anything she's done so far. Viserys became violent toward the only family he had left in the world, and eventually sold her into slavery in an effort to get the Iron Throne. Daenerys isn't nearly so obsessed with Westeros. In fact, she chose to stay in Meereen to oversee the transition away from slavery.
4) "Daenerys wouldn't be shit without her dragons, so she relies on them for everything."
I'm not even sure why this is used as a criticism. She is the dragon queen. Dragons were the Targaryen Trump Card for thousands of years, but eventually they became complacent in their rule over Westeros and stopped using them, which probably had a lot to do with why they were overthrown. Aegon the Conqueror never would have been able to conquer Westeros without the use of his dragons, and even before that Targaryens used dragons in Valyria.
The dragons are a huge part of her family's history, and they're a fundamental part of who she is. You might as well say that Varys is shit because he relies on his spies, Brienne is shit because she relies on her size, and Bran is shit because he relies on warging. Using dragons as a weapon is a skill that requires patience and practice, just like any other skill.
Some people say it's just bad writing for her to use them so often, but I think it'd be even worse writing to give her this obvious trump card and then endlessly come up with scenarios where she's not allowed to use them.
6) "Her plot is boring and feels irrelevant to the rest of the story."
Part of this is just opinion, and I can't argue with opinion (although anyone who thinks that dragons are boring should get their heads checked), but I noticed that these complaints became a lot more common once Dany got to Meereen, and there's probably a good reason for that. This should be common knowledge by now, but I guess a lot of folks still don't know. GRRM originally planned for there to be a 5-year time gap after the end of ASOS so that some of the characters could age and gain experience. This would have left us with Dany having just taken Meereen, then she was supposed to get 5 years of off-screen (off-page?) experience with being a ruler.
Q: 5-year gap?
A: It worked for characters like Arya and Dany but not so much for the adults or those who had a lot of action coming. He was writing chapters where Jon thought, "Well, not a lot has happened these past five years, it's been kinda nice." And Cersei chapters where she thought, "Well, I've had to kill sooo many people the last five years." So he ended up dropping it. He said he would have done it sooner if he hadn't told so many fans about it. And there is no gap anymore. "If a twelve-year old has to conquer the world, then so be it."
So yeah, that didn't work out too great, and GRRM ended up having to add in things that he didn't intend to go into great detail about, including Dany's rule over Meereen and Arya's training. Then a lot of what Dany was up to in Meereen ended up getting left out because it involved characters that had already been cut out of the show. So basically we were left with a season 5 that involved her struggling with the idea of fighting pits.
With that said, I'd still say that it was a necessary arc for her, even if it wasn't as exciting as burning all the Masters. She learned about the importance of compromise, her ethical framework became a little less black-and-white, and she got to deal with some consequences and struggle for the first time since season 2. That was good for her, and I'm glad we got to see it. But I'm even more glad that she's got her Brothraki back with her and she's ready to kick some Westerosi ass. Woo!
