Is it normal if i feel like i'm competing with my partner?

Its so annoying! Instead of him complimenting me back, he turns it around to himself. For example, right now I told him I was working out and my arms look great, he goes "Nah I workout my upper body tomorrow my arms look great too :)" ugh! Then other times Ill tell him what I'm eating is really good and he'll go on and show off where hes eating or where he has eaten better food of that type, ugh! Its like he gets jealous and he is insecure of himself or he doesn't like it when I'm feeling good? Idk! It just freaks me out because ever since I met him, I have had it in the back of my mind that he is gay. And this is not helping him at all. It could also simply be like said before that hes just insecure and egotistic. These were all my opinions about him in the beginning of us dating but then he showed me how much he really cares about me and was the sweetest thing Ive ever had. So when these traits come out again here and there, its hard for me to believe he might be all those things I thought of him at first because hes nice with me. Hes so into himself but I thought i could deal with it after getting to know him more but thats just not the case. It can get really annoying like get over yourself! Im the type to confront so I hope he doesnt hide anything from me because we're pretty close now and he even says he tells me more things than with his past gfs and close friends.