I don’t know what to do

It could be he just has really low self-esteem. I'm not sure. You know him better. If it's not that bad though he'll probably really appreciate and believe the short letter you write him. I think that's a good idea. No harm done in expressing what is on your heart. If he can't accept that, it is a shame.

I agree with Vivid Melody, it could easily be a self esteem issue on his part. I don't think it has anything to do with him not liking you. I know I've questioned my relationship before where I thought my boyfriend didn't like me, and he's done little things like write me letters, or tells me sweet things, that reassures me that he's there for me 100%. The key to it, is to personalize what you're saying and don't make it so cliche, make sure they can feel the love.

You should dedicate a whole day to him and just him where you pay attention to him and only him. He'll feel really loved and special and it could help your relationship blossom :) You guys will be even closer and he'll feel very much loved and appreciated. Do things he loves to do like playing his favorite video game with him or simply eating his favorite ice cream with him. He'll love it and you (:

I think he needs more validation and you may need to communicate more with him. Maybe he feels like he wants to talk to you more than you want to talk to him. So show him you care by talking and really listening. And if you really want to show you love him (or like him if you're not there yet), maybe get him a personalized gift, or take him on a surprise date, or writing him a poem or just a little paragraph like you said :)

That's horrible but maybe he's saying that because he wants to get out of the relationship in a nice way. Ask him if he loves you instead.

Be careful that he's not manipulating you with that comment. Asking someone to "show" how much they love you sounds a little odd. Its what some people to to pressure their partners into sex.