Strange behaviour during hug from a guy

"he somehow resisted and froze in place. ....."

Here is your answer, he is just a hugger, not interested in more.

There is something that is confusing me. I liked him for a long time and I thought he didn't feel the same. He must have noticed, I was obvious enough. I think he was even trying to avoid me whenever possible. Then one day he suddenly started acting close to me and hugged me. Since then he is always the one who initiates hugs. In two other occasions he acted differently: once I offered him a handshake and he pulled me closer for a hug; another time, when we were saying goodbye for a longer time he pulled me towards him and squeezed me during the hug so that our chest were touching. And now when I tried to pull him closer he froze. I don't get him. He always initiates conversations with me too.

I suspect he might be gay because of his appearance (plucked and shaped eyebrows, slick hair, has a good fashion style) and I haven't heard he had a girlfriend. All my friends say he seems gay too. But I know sometimes assumptions based on appearance are false, so I don't know what to do. I want to confess to him, but we work together... We have a lot in common, have good conversations, he is almost perfect for me. I know it is best to give up, but I somehow don't want to as long as I have hope, I just can't.

Invite him to a cafe for a cup of coffee and see his reaction.

Try asking him if he's ever been on any dating sites or dating apps. When he tells you, ask him "have you connected with anyone on the app/website" ask him about details.
Good luck

He actually might not be, if he his i think he would have been direct

Once, it was a weekend and we were almost alone at work, then he invited me for a cup of coffee at his office. I accepted, we talked, I really enjoyed the conversation. When I offered to wash the cups, he said no please, you will when you make me a cup of coffee sometimes. Then a few days ago, I asked him to come for a cup of coffee at my office these days, he said he would since he isn't so busy this week. The next day, when he was in my office and I asked him, he refused at the moment, said maybe later. But we talked, for some time. Sometimes it seems like he can't stop talking to me, he keeps talking on and on. I don't know if it's my imagination, or he is slightly avoiding sitting casually with me, but likes to keep conversations going. Like he is uncomfortable or scared what others will say if he sits with me. When we are alone he is more open, in a group sometimes he avoids even looking at me. He touched my upper back casually few times, when he was walking beside me, after the day I tried to pull him closer. But he hasn't hugged me anymore, since that day.
Moreover, I almost always like his posts. I haven't posted anything lately, except I was tagged in few, but he didn't react. Except when I posted a story and he reacted with heart on it.

Maybe he moves slower than you even though you're both moving in the same direction. Maybe you are in danger of over analyzing this thing to death. Get a hobby and take some pressure off him.

My personal opinion as I am no expert in the interpersonal relationships of other.

"Slow down, you move too fast, you gotta make the morning last ...

Months later, we kept growing closer, we talked every day, he gently touched my upper back whenever he saw me. We hugged each other, sometimes he initiated the hug, sometime I did (he doesn't usually do that with other woman, as far as I know). He seemed always happy to give me a ride in his car. In a few occasions he said that he was thinking/ worried/ cared for me.
There was this work dinner a few weeks ago and he sat down close next to me. The music was loud and we were talking almost face to face. The following days he acted as though he wanted to get closer to me.
But when I asked him out for a coffee for that weekend he said he was too busy (he told me exactly why) and suggested to reschedule it for the next week. He usually keeps his word. But the following week he didn't mention anything about that (and I didn't mention that again of course, I didn't want to pressure him).
After that, he acted hot and cold, one moment he acted interested, next moment he didn't. I couldn't stand it anymore, so I confessed I liked him last weekend at work. We were sitting opposite each other. When I told him I liked him he laughed (I guess he was nervous, otherwise it was strange), stood up and hugged me tight briefly. I told him I don't expect him to answer me immediately. Then he told me he had a traumatic experience in the past during final year of high school-beginning of college (that means at the beginning of his 20s) and since then he decided to focus on work only and spend his life that way, alone (and he still hasn't got past this traumatic experience, he still isn't ready-he is 36 btw). He added that he is scared that he may hurt or disappoint someone (because people always have expectations), that he is lame in this area (dating, love I guess) and that he isn't sure if he is the right man. He said he knows he knows that probably this isn't the right decision, but he isn't ready for anything serious since he doesn't have time (is focused on work only). He didn't say anything about his feeling about me (maybe he didn't want to say directly that he doesn't like me). At the end of our conversation I gave him a letter (I wrote it before) in which I explained all my feelings and how important he became in my life (I didn't intend to do that at the start, but I was not sure if he took what I said seriously).
And now I am really confused. I mean, he lead me on, he gave signals that he liked me. This guy is not a player, he is usually honest, kind, empathetic and I know he wouldn't hurt anyone intentionally. But I wouldn't lead anyone on and give him false hopes if I didn't like him (I would pull away, reduce contact, show him that I don't like him that way, so that it isn't harder for him in the end). I noticed that we are similar with this guy and I supposed he wouldn't do that too. And now I don't know what to think.
I thought that maybe I surprised or scared him. But I told him that I am not in a rush for anything (I wrote it in the letter too, that I don't pressure him and he can think about it, as long as he needs to).
This week we saw each other at work, we both tried to act normal, as usual. I noticed he tries to catch my eyes (maintain eye contact with me).
I tried to pull away a bit, and avoided catching his eyes in few occasions.
I am not sure in anything anymore, I am confused, hurt... but I still like him, I can't hate him. I loved him for two years.

I decided to give him a few weeks (in case he is confused) and pull away a bit. After that, if he doesn't do anything, I guess I should give up.

All the things you see as a sign that he is interested in you is just a normal relationship between coworkers who like each other, but I think you are reading way more into this.
You confessed your love to him already, you wrote a letter, you invited him and none of it was received with flying colors. He's cautious since you work together, he doesn't want to upset you but at the same token, take his subtle expressions as a NO. He is not interested to have a romantic relationship with you and the sooner you give up the better for both of you.

At this point you both can remain friends and coworkers without too much awkwardness between you. Stop it and move on!