Regular deep, slow diaphragmatic breathing is what they recommend.
There are two ways to hold your breath. The first, and what most people will do, is to seal off their airway at the back of the throat. If you ascend and your airway is closed at the throat, lung expansion injury is a definite danger.
But you can also hold your breath with your airway open and only seal at the mouth. This requires more diaphragm control because you're using that muscle to hold open your lungs. It's like the isometric version of breathing. If you ascend while holding your breath with your airway open, air will just be pushed out of your lungs and through the lips, since that seal isn't nearly as strong. This is why SCUBA divers are taught not to hold their breaths and to blow small bubbles when their respirators come out because both practices ensures an open airway. But those aren't the only ways to keep the airway open.
For SEALs, I would imagine it's important to learn to safely hold one's breath underwater. Exhaling bubbles make you visible to both other divers and those at the surface and there are times that a SEAL team would need stealth underwater. Some minimal risk of lung expansion is acceptable when trying to avoid getting killed in some other way. I had a diving instructor who had originally been trained by the Jordanian military's SEAL equivalent who would breathe roughly once per minute. He said it was second nature based on his training but that we should learn to breathe the way PADI recommends since no one would be shooting at us.
You cannot conceal bubbles while on SCUBA.
Never hold your breate while ascending =/= Never hold your breathe underwater.
And, said in a less snarky way: I can see why a diving instructor would say "don't hold your breath" when you're under water. Navy SEALs likely dive a lot, but they also do training and actions above the water. And they likely spend a lot of time in stressful situations (certainly more than me). I can imagine they might box breath _on land_ to help manage the stress.
I have 5 classroom sessions of about an hour each and two pool sessions and 4 open water dives to take you knowing nothing to keeping you from killing yourself.
When I first got certified as a diver, I would suck down a tank in 15 minutes. By the time I became an instructor, my longest dive on a single tank was close to 1.5 hours and I had plenty of air left.
It would be pointless for me to try and teach breathing control techniques I was using by the time I became an instructor to an Open Water Diver student who will be lucky enough to remove and replace his regulator to pass the course.
We teach not holding your breath because most inexperienced divers will default to panicked fight or flight the second anything goes wrong.
Believe me, I’ve had to physically restrain students underwater when the reg fell out of their mouth and it took them more than 2 seconds to find it. They immediately want to shoot to the surface and 100% they’ll be holding their breath (another aspect of panic) if I don’t hold them down, put the reg back in their mouth, and calm them down.
Breath in, you begin to ascend. Breath out, you will sink.
Your goal is to find a breathing pattern that allows you to stay neutrally buoyant so you’re not fighting the rise and fall by swimming against it.
Part of the instructor exam, at least when I took it, was a pool session where they tested your ability to achieve and maintain neutral buoyancy.
You would sit cross legged holding your fins for balance like a meditator half way between the bottom and the surface and you could not rise or fall more than a foot.
It’s something a lot of divers also practice when doing safety stops. Even if there’s an ascent line, many will simply stop at 15 feet, and watch their dive computer trying to maintain exactly at 15 feet using only their breathing.
The reason for that is often there will be no ascent line or you may have to do decompression stops in open water with no physical point of reference.
In the emergency ascending you are suppose to constantly exhale all the way to the surface. otherwise your lungs might tear.
When doing next dive take a balloon with you and fill it with your air at the depth. Then go up.
Otherwise when at same depth you don't have to worry too much about it.
Disclaimer i am not an actual certified diving instructor.