However, if you have tremendous knockout power, than a few good punches is all you need in a fight...and where boxing is a real advantage.
UFC fighters don't have their hands up because they are a bunch of wrestlers & martial artists trying to act like boxers at the start of every fight/round. They're kind of like video's you see of two goofs feinting and bobbing & weaving 5 ft. from each other during a stupid street fight.
It feels awkward because your mind hasn't grasped learning the basic techniques of hand placement and throwing punches. You may just be a slow athletic learner and need to spend a lot of time out of class understanding and reinforcing what you were taught. Athletic learning is just like anything else in that people learn at a different pace, have gifts that make certain sports easier to grasp AND learn best under certain conditions.
Edit- Easy Tiger, don't confuse my statement of being a slow athletic learner with being dumb or stupid. You said yourself that you're having problems with awkwardness, all I provided was an athletic reason why and gave a solution. That natural reflex you speak of isn't natural, it's a learned movement and as such its important for the athlete to understand what type of learning conditions are conducive to success and what type of practice is needed to get something down. If you don't one of two things will happen after frustration kicks in 1.) You'll quit and move on to something that comes easy to you or 2.) You'll say screw it and do things your way to the point of almost completely abandoning the technical side.
You clearly know very little about fighting. Anderson Silva throws quick straight counter punches and KO's people. He leaves his hands down and gets KO'd. If you go into a street fight against someone who can box swinging like a retard you will get ****** up. If it was inconvenient to keep your hands up then why do the majority of fighters from all disciplines do it?
It may feel that way, but it does work. Look what happened to Amir khan and his cousin when 8 gang members tried to car-jack them in Birmingham, UK. Both are boxers, and they battered 8 of them between them, and walked (or in this case drove) away without a scratch on them. It goes to show that used properly in a street fight it can be very effective.
Don't box in a real fight. Get right into it. Headbutt right into the nose (HURTS LIKE HELL). Make your hand like a fist and punch right into the nose (Won't hurt your knuckles). Elbows (More devastating damage to your opponent). This is what you should do. But your boxing training will help because you will have great rhythm.
If it feels awkward then you're not doing it right. Trust me it was like that for me too, except for me it was all about foot positions. Eventually I found my balance and my footwork is now pretty damn impressive if I do say s myself
I've been taking boxing classes for about 2 months now, 4 days/week, and it still feels awkward - more awkward than throwing my own kind of punch, the kind my body is naturally inclined to throw (a haymaker or even a quick and messy jab).
All the having your arms up resting near the sides of your face gets tiring and I find it makes my punch less effective and less fast. I can't imagine how boxing could be used in a real fight - it's a bit slow-paced if you're comparing it to an opponent who's just swinging randomly and very fast. Your punches are structured, being the boxer, and that structure can take away from your body's own comfort when it comes to speed. PLUS, your arms won't get tired from having them raised during the fight. I know that your chances of getting hit are higher without the arms, but it just seems very inconvenient to have up.