Hey Devil! I've done a lot of swim coaching over the years (lots of different body shapes and sizes); the only place I ever heard people think they can't either tread water or float is the military.
Here's what can narrow down where the failure point is that is making you sink, is.
Typically it's either tensing up because the person doesn't like the way the ears feels when their ears are submerged in water.
Start with:
1. Wall drill shallow water
2. Wall drill deep water
3. Floating
4. Treading
If you don't like the way the water feels in your ears, it can make your whole body tense up.
Get ear plugs that are formed inside your ear for "swimmers ear," that will keep water out, if you are able to use them during whatever swim qual.
If they are not authorized, don't train with them.
Get a Swimmers Ear product to dry your ears out.
Task Breakdown:
If you can't float without effort, try this:
1. Get in the pool: go to the side of the pool.
2. Grasp the pool lip with two hands shoulder length apart.
3. Bring your knees halfway to your chest.
4. Your ass is going towards the pool floor at this point.
5. Place the balls of your feet on the pool wall about hips width apart.
6. You are looking straight ahead at this point.
7. Once you are solidly on the wall, move your whole head and neck backwards into the water. You are now looking at the sky/ceiling as far back as you can, but your neck is not overextended.
8. Both of your ears are fully submerged in the water.
9. Get comfortable. You should be entirely relaxed.
10. When you are comfortable, bring your head straight back up, looking straight ahead.
11. Now, shuffle down the wall moving your hands and feet, still making contact with the wall, to the deep end.
12. Do the same thing, until you are comfortable with both ears being totally submerged in the water, and your body is entirely relaxed, with the correct form.
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When you are confident, comfortable, and relaxed with the above task sequence, the next task is doing the same thing, modified ending with floating on your back.
Your head position on your back will be the same as when your ears were fully submerged and you were on the wall.
Holding onto the wall, fully extend your arms.
Use the balls of your feet to push off the wall.
You will now be in the horizontal floating position.
You are going to swing your feet down towards the pool floor, and your top half moving upright. You're staying relaxed.
Now begin bicycle peddling with your legs.
Now take both arms and make the motion of stirring two huge cauldrons. Your palms will be flat on the surface of the water.
You have to be super relaxed. Try for very short amounts of time, and stop.
