How do I handle a guy who likes me but is too afraid?

I kinda like him, and I've made this clear on several occasions. He says he likes me since the very moment he saw me because I have an innocent soul that shows easily. However he says he's been trying to avoid me as much as he could because he doesn't want to get attached and that he's emotionally fragile and scared that I'd reject him because he doesn't want to lose me. I didn't know how to respond then so I just went silent and agreed that I wouldn't want him to get hurt and that I liked his honesty I want to get closer to him, to give us a chance, but now I don't know what I should do?

How do I handle a guy who likes me but is too afraid?
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