Why are so many service members refusing to receive the COVID vaccine?

Think of it like a flu shot. It will reduce the likelihood of catching it in some circumstances and if not it may or may not reduce the severity.

I’m in multiple demographic groups and got the two shot series, one booster. The second shot gave me permanent side effects. Also collapsed while at the VA and ended up hospitalized for 5 days. So, I do understand the reluctance of many to get the shot.

It did prevent me from catching Covid several times already.

Could it be the unpublished side effects? When I received the second Moderna shot, I ended up hospitalized for 5 days. That shot caused orthostatic hypotension (low blood pressure). Think BP 70’s/30’s. Couldn't stand up without assistance., couldn’t function. Others have had similar experiences. I had a team of doctors and including a doctor of pharmacology trying to figure out a cause. Med manipulation, physical issues that I have had for years provided no relief or explanations. The only activity different was receiving that second shot. They discharged me still having low blood pressure and two years later I still have daily episodes of blood pressure drops routinely in the 80’s over 40’s.

Speaking as someone who knows what it means to be on the short end of the 5 (or whatever) percent who have an extremely adverse reaction to some prescribed medication (e.g. severe hallucinations induced by a fluoroquinolone antibiotic), I don't consider getting vaccinated to be as much of a "no-brainer" as the public-health experts (and news media) make it out to be.
If you pay attention, the public-health experts, and the regulatory agencies, have gone from "prove no harm" bias to presuming that the vaccines are safe except where demonstrated otherwise. Hence we get admonitions from the CDC or FDA for people who have a history of allergic reactions to any of the vaccines' ingredients to decide carefully -- minus any specific information about what those ingredients are. That's a subtle, but potentially very significant, shift in bias.
Then there are the still-unanswered questions of how to weigh presumed but unknown long-term efficacy against the equally unknown risk of long-term (or even slightly delayed) adverse effects.
All of which has me not saying "Hell no!", but also not at all inclined to push my way to the head of the line. Call me selfish, but I'm perfectly comfortable letting millions of all you more-eager folks play guinea pig before I roll up my sleeve.

I got my first dose this morning but I'm a member of the old folks club. So far no problems. I did take a Tylenol when I got back home.

My understanding is that no Service member in uniform can refuse any vaccination without repercussions' In other words if you are done with being in you will be assisted out if you refuse. The military does not have a sterling reputation with vaccines as shown in history. If given the choice to decline I would but I am retired and I won't be volunteering for the VA to test on me. My understanding that almost all military age folks are not in the danger zone with this flu and a great deal of the fear mongering going on is not helping.

I quit even taking flu shots way back in 1971 or so. The reason is simply because they don't know diddly about viral infections and are just guessing. I never signed up to be a lab rat for anyone. Despite the billions of dollars of economic loss due to common colds each year, they're still around today. If they could cure colds colds, then they might know something but until they can do that, they're just guessing.

You did the right thing, but you don't get a cookie.

Active duty, reserve and guard are required to be vaccinated. Those fools that do not should receive a bad conduct discharge; period. This is a mandate, therefore it is not open for discussion

I refused but honestly if I could refuse any of the shots I would. I never got sick until I joined the army. I never needed shots because of how I took care of myself. Even a room full of sick people. I just don’t think I need to be forced into something that is not necessary for me. My family is the same way never sick.