For the very reasons identified. People want it to be true, without proof, because believing it is true serves a psychological need that provides a fake pay off. It's not "your fault" you didn't make progress in that algorithm, because "the universe" conspired against you and "P != NP", you're off the hook.
Getting off the hook like that is so much easier than facing your own responsibility.
I understand it's very compelling to believe this for that reason, and yet, to do so doesn't work to actually make progress. I understand the psychology. People will fight this to the end to preserve their sense of zero responsibility, to shelter their ego. So much invested, so many layers of justifying narrative, already deposited.
I'm not saying it's right or wrong what you choose to believe. I don't think you need to feel bad about it. You can choose to live your life however you want. If you want to believe P != NP without proof, you're just not someone who is mentally equipped to create innovations in that space. Does that make you bad? No, it's just your choice. You already made that choice. No need to deceive yourself about it. Can you really feel an absence of shame however, trying to talk other people out of it? I guess that is what I am campaigning for.
Believe whatever you want, you've already made your choice. When that young student comes to you, and you try to talk her or him out of pursuing this to preserve the narrative you've already subscribed to yourself, that doesn't work. So if you are aware of how it's your belief, maybe you'll give them space for their belief.
That awareness, and awareness toward others.