I've failed to successfully train some.
Nice line, Sam. It is important to remember that with the vast majority of agencies, there is no failure. The student has the option of continuing to work until he or she meets the standards. Ideally, we instructors can use our vast skills (

) to bring anyone to a passing level. In reality, some students elude our best efforts.
I had two very unrealistic grandparents try to get through to the confined water (referral) level in the few days before a planned family trip to Hawaii. The husband was not doing badly, but his wife, who had had a double mastectomy less than a year before, was struggling and growing exhausted. She finally conceded that she wasn't going to make it and dropped out so that I could go on with her husband. It was at that time that they revealed that the pool sessions were the first time in her life she had ever had her head fully under water.
I had a 13 year old boy show up for the academic sessions without having done any of the knowledge reviews. He swore he had read everything and knew all the answers, but he was obviously lying and didn't have a clue on most of the answers. I learned that this was a troubled youth who was staying with his aunt and uncle, who thought that getting certified so he could dive with them would help him. When we talked, they agreed that he needed a more mature attitude and withdrew him from the class.
I have a 17 year old boy in a cold water OW session whom I had not had in the pool. He had poor mask skills (and his other skills were weak), but he got through until he finally could not do the mask removal skill. This was the last session in the fall before the reservoir closed, and he decided to finish the next spring. I don't know if he did.
We had a brother and sister with different degrees of autism. The sister eventually got certified, after many, many sessions. The brother ended up with the scuba diver certification after it was clear to everyone that he should always dive with a professional.
I have had a couple of others with situations similar to what others have described.
A few years ago a SB poster working on his DM certification made a post in which he talked about how common it was for people to drop out during the first pool sessions. Apparently at least one person did it in nearly every class he had observed, and he assumed this happened everywhere. I said this was very unusual and indicated something was wrong with the operation through which he was being trained. Instruction properly done should carefully guide students from wherever they are to where they need to be, and only a small minority should exhibit insurmountable problems.
He disagreed, arguing that scuba standards should be rigorous, students should not even start instruction until they could meet certain high standards, and the operation with which he was associated was doing students a service by weeding out the unfit early. If someone has that philosophy, they will not only experience a high failure rate, they will be proud of it.