As a wise mare once said: opinions are subjective.

that’s just your opinion

@The_Mungoman  
Hence why it’s better to study differing opinions than to mock them.

@Background Pony #3D61  
I can agree with that. I’d say understanding and empathy should not be forgotten in these cases.

@The_Mungoman  
The problem is that a person acts like their opinion is better simply because they have more thoroughly explained it. Perhaps their opposition actually has better reasons, but is less skilled at putting them to words. And if anyone says “X is the best movie ever”, I would ask them: best at what? That is the heart of subjectivity. We seek to measure the value of things, but we fail to measure all possible kinds of value, and the inconsistency from one person’s experience to another’s creates differences in perspective that are often impossible to fully rectify.

@Background Pony #3D61  
I don’t think the length of the explanation is the important factor of this. It’s more about how much sense said explanation makes.  
To go with your example, does it truly make sense for Thomas and the Magic Railroad to be regarded similarly as one of the best films of all time as The Third Man, for example? What would the argumentation to prove so be? Is that argumentation sound?  
You are correct, an opinion does not become less subjective when supported by logic and fact; It just becomes more robust. I think that’s the point being made here.

That “wise man” sounds like he thought too highly of himself.
 
You could talk for three hours, write essays, and go into extensive detail on why Thomas and the Magic Railroad is the pinnacle of cinematic achievement and you still wouldn’t become the world’s foremost film critic. An explanation doesn’t remove the subjectivity of an opinion, it just makes it easier to understand.

With a shovel?

+1 to the OP
 
“That’s just your opinion” is a thought-terminating cliché, like pretty much anything that comes out of a SJW’s mouth/tumblr. The correct retort is along the lines of:
 
“Even if it is, that does not mean that what I said is invalided by being my opinion”

‘thats just your opinion’ i get so tired of hearin that every time i try to have a serious discussion with someone with problems i have with pics.  
every fricken time i make a comment about a problem with a pic someones gotta disagree and when i come up with a elaborate, well thought out, logic to explain my argument all they come back with is ‘well thats just your opinion’.  
that or they say somethin stupid like ‘this coming from someone who cant even use punctuation’ as if that has any relevance to the discussion.

@Itsthinking  
reminds me of that dancing dog… thing…
 
ITS PARTY TIME!

Well, time to face-rape Letrotski.  

@Millennial Dan  
The opinion that you’re going to describe as “better” is going to be invariably colored by your own views and how much of an open mind that you have.

@Background Pony  

@ClownDicks  
Perhaps, but in a case like the one I described, who’s to say which opinion is better?
 
Don’t get me wrong, I don’t like cop-outs any more than you do. I’ve typed out paragraph after paragraph of what I hate about MMC, for goodness’ sake.

@PonyPon
 
Internet arguments: the only winning move is to not play.

@Itsthinking  
Technically he won.
 
He kept his viewpoint.
 
But he lost by forfeit.
 
There’s no real winner anyway.

@ClownDicks  
Ah yes, but what if one proclaims “victory” and constantly says that the boredom of the other side shows that they have a faulty opinion?
 
Again, these are all things that I’ve seen firsthand.

There’s forums for this stuff.

@Millennial Dan  
Even so… again, not all opinions are equal.  
@Itsthinking  
Neither. They just got bored.

I dislike tomatoes. They are flavourless to me and I dislike the consistency.  
My father, on the other hand, can’t get enough of them.
 
Now, is either of us wrong?  
No. Because as much as I reason my point as to why I dislike tomatoes, doesn’t give my father any reason to stop liking tomatoes.

@PonyPon  
If one of these people gets bored of the discussion and just walks away, did they “lose” or did they see an argument that they were pigeonholed into not winning and realized the futility?

@ClownDicks  
Trying to form logical arguments are great, but lately I’ve seen some people mistakenly confuse that with matters of subjective taste. For example…
 
Person A: I liked Sunset’s demon-succubus design at the end of EqG.  
Person B: Well, it was a terrible design. It reminded me of (blah blah blah).  
Person A: That’s just you’re opinion.  
Person B: No, it’s the honest truth.  
Person A: I disagree.  
Person B: Well, you’re wrong.
 
Etc.

@Itsthinking  
Then I hope he/she doesn’t get too invested.

@ClownDicks  
It depends on the opinion. People like or dislike things for different reasons.
 
If I were to look at a painting and say “I like this painting because of the use of color,” and another person says “I dislike it because of how the background is painted,” are either wrong?
 
They both have reasons, but what if the person who likes the painting disagrees with the person who dislikes it and makes it his mission to change that person’s mind?