Another Calming Example

it was explained to me why my concerns were wrong

Not sure if what I have in mind is the same, but I can think of scenarios where an explanation of how I'm wrong makes it feel like my concerns are being dismissed instead of being addressed. I'm guessing it's because a child's reasoning can seem illogical to an adult even though they actually make sense from the child's perspective, and it's upsetting when adults fail to acknowledge this.

Notice that jefftk is responding to the child from the child's perspective. The child thinks that there's not enough pasta, presumably because of what they can see from the serving bowl. jefftk shows the child the extra pasta in the kitchen (so the child can see that there's actually more pasta), thus addressing the child's concerns.

In contrast, one may answer from the adult's perspective instead. For example, they may say that there's enough because one serving of pasta is x grams and they made 10 servings when we have only 8 people. Or maybe they say that it's made by grandma who has lots of experience in estimating how much everyone needs. These make sense from the adult's perspective, but if the child doesn't really understand or trust the reasoning (e.g. because they don't have the concepts yet), then such explanations would feel more like dismissals of the child's concerns.

the message I received was that my concerns about [issue] were to be kept to myself in future

That is not a message I would want to send, and I don't think it's a message I sent here? I listened to their concerns, and then specifically addressed them, making sure to get buy-in before doing anything.

You have to realize that as a parent you deal with this situation on a daily basis: Kid is hungry, does something unreasonable, get's upset about the resulting conflict. 

You can't do a psychological deep dive everytime. If this isn't a recurring theme there very likely is nothing more to it than hunger+conflict=upset and calming the kid down is exactly the right thing to do. 

In your case it seems to have been a recurring thing and as a parent you should catch that, but, in defense of your mother, she probably calmed you down a thousand other times without leaving any psychological scars (or even memories).

Several times you mention that it sounds like I was pressuring them, but this whole interaction was optional for both of us. I was offering to listen to them and try to help, but (they knew that) there wouldn't be any consequences to telling me they didn't want help beyond me just going back to the table.

It looks like you pressured the kid to stop crying and just hide their feelings ("I told them that I couldn't understand and asked if they could speak normally").

Would you feel differently if it was actually the case that I was bad at understanding kids who are currently crying?

it seems unlikely to me that the kid's real reason for getting upset was that "they were worried the pasta was going to run out and they would still be hungry after dinner"

Agreed. This is why I wrote "I think this is very unlikely to be why they fell apart while at the table"

I infer that either you, in this situation, or the kid's social environment, before this situation, pressured the kid into generating fake but socially acceptable explanations of their feelings.

I think this is a weird and complicated question. When you ask someone why they are upset, especially a kid, often you will get something that is not the real reason. People have limited introspection, especially with only a few years experience. So yes, I don't like the thing where asking someone what's wrong can decrease both their and your understanding of the actual problem.

On the other hand, when there is actually something important wrong, kids can often describe it well. If you look at the complaints adults give about the treatment they received as children, one of the biggest ones I run into is adults not listening and taking them seriously when they described problems.

So the approach I've generally taken is to talk to kids and help them solve the problems they say they have. This generally seems to work pretty well?