Their s/o is scared they'll leave because of their insecurities
Would know of your insecurities but not think much of it, taking it upon himself to remind you that the things you're insecure about are either nothing to worry about or something that doesn't matter to him. But as soon as you voice your worries of him leaving because of something you don't like about yourself? He'd sit you down and lecture you and afterwards have a talk with you. He'd let you know that those thoughts aren't true, he wouldn't leave you. He loves you for you, and some silly insecurities wouldn't change that.
"The most important thing is that we love each other, insecurities or not."
I think it would come out during an argument, which would most likely be one sided. You had been acting off and he took it thr wrong way, demanding to know what was going on. And you just snapped, comparing yourself to him and telling him that you wouldn't blame him if he decided to walk out on you. He would take it kinda personal, but push that aside to seriously tell you he wouldn't have gotten with you in the first place if such things would bother him. He chose you for a reason, he doesn't change his mind so easily.
"You think I'd pick someone who i didn't think deserved me?"
He noticed you being more distant and sees you paying more and more attention to the thing he knows you're insecure about. He would let you be, passing small comments here and there to put that thing in a positive light. But as soon as he'd notice you acting off, like the insecurities are really getting to you, he'd step in. He'd be blunt about it, not cutting around the chase and saying things as they are. He'd remind you that he doesn't see those silly insecurities, and that to him you're amazing, his favorite person.
"Besides, you're not getting rid of me that easily."
To him you're perfect, the one and only for him. Beautiful, kind, funny and the love of his life. He wouldn't see a thing you should be insecure about, he sees nothing but stuff to love. But he isn't unfamiliar with insecurities, he has them just like any other person. So while he doesn't see it, he would understand you feeling that way. It hurt him, but he knows insecurities are a human thing. But finding out you actually fear him leaving because of it? His heart could almost be heard breaking as you cry in front of him, voicing every thought you've been bottling up. And honestly? I bet he tears up himself as well. He'd do anything he could to remind you he loves you, and to him you're beautiful, in and out. He'd voice everything he loves about you, even exaggerating every now and then.
"Even if you weren't gorgeous, your amazing personality would make up for it. But you are, you're beautiful inside and out."
Jimin would be the same, having insecurities and being scared you would at some point acknowledge them as well. Sometimes it would lead to him being clingy, and sometimes he would distance himself a bit. At one point when he did the second is when he'd find out about your feelings. It would take him walking in on you breaking down to sit down and have a proper talk. Both of you would open up about the insecurities you feel and the fears that came with them. It would lead to both of you reassuring the other, making sure both you felt better about all this. From them on your communication would improve and your insecurities would be talked about.
"I did not think about what my actions would do to you, y/n. I'm so sorry."
He has overtime grown to accept and embrace his imperfections, knowing they're human and can't be controlled. Pimples? No, they're new friends and they'll leave at some point. Gained weight? At least I'm eating well and being healthy. And he took it upon himself to teach you to feel the same way about them. Once he finds out your true feelings and fears he will be very strict with you. He'd list the things about himself that most would see as insecurities, and name the things he's still insecure about, making it clear he has it too but that it's normal. He wants you to see your imperfections as things that make you perfect.
"I would never leave you for such insignificant things."
Being the "golden boy who can do everything" comes with its perks, but also its downfalls. So much pressure is being out onto him, which leads to more and more insecurities. But still he doesn't deal much with your insecurities. He has a way of living and being around you that you almost forget about said insecurities and feel wanted around him. So due to that he wouldn't really know what to do when he found out about all that. I could most likely see him adoring you, telling you everything he loves about you and in the meantime talk bad about himself. He would hope it'd make you feel less bad about yourself. And in a way it would help, knowing that those things he said about you are mostly true in his eyes.
"You're basically perfect! Unlike me who-"
