I often find this aggravating, but in some cases, I think that stating an opinion as being unpopular is a defence mechanism that may stem from previous responses to said opinion.

On the topic of everyone being busy, for example, a friend once shared a similar opinion at work and their colleagues jumped on that opinion and argued against it in a manner that was effectively dick-measuring about how tired and burnt out they are, but how they're going to take on more work nonetheless. It was an especially toxic work environment, but it's not abnormal to find people who seem desperate to sacrifice themselves on the altar of capitalism.

I speculate that some of this bizarre defense of hyper productivity arises from people who are forced to work that way for so long that they start to think of it as a thing they choose to do. My friend was fortunate enough that he was able to quit his job to stay home with his newborn child, but far too many people don't have that opportunity. I wonder if some of the men who mocked him for quitting the job did so because they wish they had been able to do the same thing, but given that that ship had long since sailed, pretending that they chose to stay at that shitty job helped them to weather the stress.

This is all a long-winded way of saying that I sympathise with people who hedge their beliefs with saying an opinion is "unpopular". I think that sometimes, it's a way of saying "this is something I believe, but I'm not actively trying to change your mind about it". There may also be an element of someone hoping that people will say "idk what you mean, that's not an unpopular opinion", in search of validation. That's annoying, but I'm sympathetic towards someone fishing for validation in this topic, at the very least.

But then how is someone supposed to argue about how how the sky is red sometimes?