Friend thing? i'm confused?

So me and a friend(probably my closest) have been in a huge argument and both of us did something wrong. I admitted mine and he never admitted his, which is pretty dumbfounding, but anyway, we sit at the same lunch table, even after the argument, we just don't talk. so today, he was just sitting there staring at me. Legit staring at me like an owl for about 5 minutes and it was creeping me out. no one else noticed lol and it was pretty awkward. What was he trying to do? read my mind? can u help me?

Also, I really don't want to lose him i knew him since we were 4 and now we are almost in high school. How can we solve this?