Should I move on and forget about my crush?

It's been a month now since I confessed to him. He was insecure since his past "lovers" were a little too rough but I was making sure he would never feel that with me since I'm different. He was cold but sometimes he would show me affection, hugging me, kissing me and whatever. On Thanksgiving I wrote him "I'm thankful for meeting you" but he wrote me "Thanks for your friendship"... All my friends have been telling me he friend zoned me, but I just can not believe it. Anyways, it is not the first time he acts like this all suddenly. Sometimes he's on the phone smiling and everything, he's always online and if I do not text him, I don't even receive one accidental text from him. On person his different... but on my back, he's soo cold. I am really tired of this, I have spoken to him about this and he says "You have to give me some time"... But that is not a reason to treat me this way, right? Or maybe I should wait and stop complaining?
Should I move on and forget about my crush?
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