Accepting criticism as a DM

So, 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 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?

Edit:

Also, I should say that 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.