No one here can really know you well enough to tell you what's 'making you feel weird' but if it were me I imagine it would most likely be one of two things:
I feel weird because same-sex dating is very harshly socially judged. If I identified this as being the reason, I would try to convince myself to push forward with the relationship. With some people though, if they aren't able to push that awkwardness away eventually, it might affect the relationship negatively - and maybe that's why you don't want to do it, because you don't want to make your partner feel as if you are ashamed of them. I never felt this way when I dated another female when I was a teenager, maybe in defiance of my parents being so degrading about my sexuality - but it's understandable that you might be nervous in the face of surprising people with something they might not know about you and you're not sure will make them uncomfortable or not. Just try to remember if this is the case that people who will mislike you for it aren't people you need in your life.
The term 'friendzone' can be a somewhat heavy topic. Maybe my general dislike of it is what's making this part stand out to me; I might be misinterpreting this completely. Regardless, if you feel like turning him down is 'friendzoning' him, I would assume that implies guilt for following your emotions. I think it's worth pointing out that you don't owe him anything like that, and if he's your friend he will understand. Again, maybe I'm misinterpreting that, but hey.
Or, similarly, this could be less of a 'I feel guilty about friendzoning him' thing and more of a 'I feel guilty about not wanting to do this because I owe him emotionally, but I'm currently depressed.' If this is the case the same general idea still applies, and if you explain it to him he should understand. If he doesn't then he's not really worth your time.