Private training works great for obedience training when you need to learn how to train your dog to do some obedience commands.
It will work for simple behavioral issues such as pulling, jumping, barking…etc as well.
We can also use private training to help human who are knowledgeable and experienced. For example, I have done a lot of private lessons to help other dog trainers.
You can think of it like living in a house that requires some work.
You can learn how to do simple DIY jobs yourself when your house needs simply repairs. And it will work. But most people cannot redo their entire electrical system, change the furnace and the HVAC system, and completely upgrade the plumbing system all by themselves. They can learn and try, but the result is probably not going to be at the same standard as a professional job.
Also, when things are falling apart, fixing only one thing is likely not going to solve the problem. Some jobs would need to be done in a particular order, and it may involve fixing some other things that may not look obvious.
Without the proper knowledge and experience, the situation can become worse and further damages can be done, not to mention they and their family can potentially get injured during the process.
Board and train allows the trainer to get to the root of the problem and rebuild everything with a strong foundation at a professional standard for the clients.
Once the house has been rebuilt — and everything has been done properly — the owner can then maintain the house doing things that they are fully capable of doing (e.g. change the air filter every 90 days). They can also decorate the house to make it look better without having to worry about things like leakage and water damage anymore.
Similarly, after a proper board and train, the trainer can teach the owner how to keep up with the training so the owner can continue to work with the dog, teach the dog new tricks and go for more exciting adventures, without having to constantly manage and avoid the old stressful issues.
A proper board and train program should provide proper support to the human. The difference is the human is being trained to maintain the building after it has been set up professionally rather than on how to take down and rebuild the entire house.
Instead of having to dig up all the old roots of the trees, remove all the weeds and dead bushes, install an automatic irrigation system, build a deck, … etc; the owners only need to cut the grass and trim the plants regularly so they can spend their time enjoying their beautiful garden.
Also, imagine how much longer it is going to take when you try to DIY your entire own house as compared to hiring someone to do it for you professionally?
With some DIY house jobs, taking longer is not a problem (e.g. gardening, painting). But it is not the same with dog rehabilitation. A dog who exhibits behavioral issues is a dog who is suffering emotionally and psychologically. When the dog is obviously suffering, why would anyone want to prolong the agony and make the dog suffer longer unnecessarily?
Hope this makes sense.