He can't be vulnerable?

I'm very confused and I know he has a good heart. But he seems to be very insecure and afraid to "look weak" in situations. To be vulnerable, it takes a lot. We've been seeing each other for 2 months, we're coworkers. He's been the one to ask to see me every single time for around 10 times total now. He'll say to our mutual friend coworker "I think I've won her over now because... XYZ", or asks her constantly if I talk about him to her or if I've said anything good about him. He always stares at my face, even from across the room at work. Or when we hang out he'll just sit there and gaze at my face. We'll do things too so it's not like i'm being used- we haven't even slept together yet but it was getting close to that point.. .

So I decided to ask him to hang this time a few days later and he said "sure let's do it! I'll let you know what days I'm free." and he got back to me with days. But also added "Due to miscommunication I also need to verify you understand we're strictly platonic." At first I thought it was a joke. But he repeated it, so I said "I appreciate your honesty with me but with my kindness, beauty, and affection I don't want to be taken for granted so we can stay friends but I'm not looking to hang out sorry." He replied "Gotcha." and that's it... but then my friend texted me a few hours later saying he asked her again "if i've said anything about him."... I'm so confused on what he's trying to get from this. Why even ask if I'm dropping it respectfully for him... I know he can be very insecure with himself. And also with emotions. I just never pressured him with anything whatsoever. And he was the one to talk about me to all his friends and our mutual friend constantly and once when he thought he was losing me he tried really hard to be vulerable and show he had feelings. Everyone has said they think he really likes me... I'm sad because things seemed to be great. :(
He can't be vulnerable?
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