She was toilet trained by 3, I can't remember exactly. My daughter was in a preschool from 2-3yrs and I think that helped a lot as well because *everyone else was doing it.*
I think that you are sending him the message that he can urinate almost anywhere (bathtub, cup, toilet) when there is really only one place that is hygienic and acceptable and that is the toilet. I reread your post and you've only been addressing this with him for a few days. It probably takes longer than a few days for him to overcome his anxiety or discomfort with the idea, and I think he definitely needs some proper instruction as to how to succeed.
Give him a few basic nonnegotiable instructions (close the door, sit on the toilet, wipe if necessary, flush, wash hands). It's a set routine, it's not up to him to decide where and how he goes; he will have to use a (semi)private toilet facility and observe good hygiene in elimination if he is going to succeed in life. He may be feeling weirdly confused because he probably realizes that adults don't pee in the bathtub or a cup and doesn't know how to gain any skill or confidence with these mixed messages.
You could tell him that young men and women do things to take care of their bodies all by themselves, and it's time for him to take charge since he has shown what a responsible little guy he is in so many ways (find some examples). There are things he will not be able to do if he continues to wear a diaper (school is one). If he wants to have more opportunities and independence he will have to learn to use a toilet. You can explain this to him.
Toilet use seems to be a big area of anxiety and frustration some for kids. You can be assured that he will not be going to work in diapers
, so he will get this business resolved eventually. Be patient & don't feel pressure. At his age he will probably take to it right away when he decides the time is right.