I've been running two campaigns as a DM for about 7 or 8 months at this point. I've been running it with 2 different groups.
The problem that I'm facing, currently, is the perception, from some members of my second group, that I'm not receptive to criticism.
To elaborate, some of them believe that whenever they have criticism for me, it's always valid and I should be accepting of it.
For me, the way that I handle any form of criticism in my academic life is that each person criticizes an individual based on information that they know. So, they point out inconsistencies in whatever they're doing based on information that's available to them. That individual is, then, allowed to give them further information so that they can change their criticism or retract it.
I've criticized, say, someone's proof before in Mathematics until they pointed out the underlying thought that they had behind a particular sentence and after that, I've had to retract that particular criticism since it really isn't valid.
I've tried to bring that into my D&D life and, even as a player, I tend not to criticize the DM about story-related material, prefering to work through the tale as a character to its end before analyzing it. My criticisms have always been restricted to the gameplay of the story. Of course, that's just a personal thing and I don't impose that on my players at all.
My first group happens to understand this really well and is receptive to any discussion that we have regarding their criticism after the game. So, the members are entirely ready to retract their criticism if I can convince them that it's not valid (at some times, I just can't argue with what they have to say, though, so I don't argue on every point).
Some members of my second group don't believe that this is how feedback is supposed to work and they believe that I should be changing my style of running the game based on their preferences. The other members disagree with them and have told me that while there are improvements that can be made in the gameplay, the approach I have to taking criticism is just fine.
So, at this point, I'm kind of at a loss on what to really do? How should I approach them? Is my entire approach to D&D wrong?
Also, whenever I have private exchanges with these members over a particular thing that's bothering them, I tend to try and look for a second or third opinion on what they're saying so that I'm not misinterpreting it and unreasonable disagreeing with them for no reason whatsoever.
That is, I will usually show others the messages that were sent between that member & myself regarding that topic and will ask them for their thoughts on the entire issue. I try not to restrict myself to just describing the exchange verbally, because I'm not quite sure that I can give an honest recount of everything that has occurred. I'd rather show them the text directly.
I'd like to thank everyone who gave an answer to this question and the various comments that I made on each of your answers. What I've gathered from reading the answers and the various comments associated with them is the following:
I should make it more apparent that I am accepting their criticism. I should not attempt to argue with the group about what they didn't like.
If there's a bit of criticism that I get about something in my game and it won't exactly help my game or help me have fun as well, then I should do my utmost to bring about the maximal amount of changes such that my players will be happy and I will be happy.
I should not treat criticism in D&D in exactly the same way as I would treat academic criticism since the former is highly opinion-based and the latter is academic in nature.
I guess I should also add that the main trouble that I have is mostly because of my general approach to literary works as well? Like, when I read a book or watch a show, I tend to reserve all negative judgement specifically about the plot until I have reached the end of the show.
So, for example, I will notice things that weren't explained and will discuss them with others, under the assumption that the creator of the work will explain them later. I will form opinions about the characters or lore but I will not say 'this doesn't make sense' until I have reached the end.
In a way, I think it's rather unfair to the author to just make everything in their story seem like it's a plot-hole. The author had the patience to write the story, so the reader should have the patience to work through the story if it interests them.
Obviously, it doesn't have to always interest the reader. Like, just because I find a book uninteresting doesn't mean it has plot holes. But yea, i guess the 3 points I mentioned above are my main takeaways from this entire discussion.