Hi! I'll be glad to be of help with this issue.
I can imagine how frustrating this situation must be for you. You are clearly a normal young person and you are being very patient and understanding about your partner's sexual problems.
It seems from your description of his ability to ejaculate through masturbation that the problem is indeed psychological and not physiological. So that gives us a starting point to work from. But it also means that the resolution will most likely be a slow process rather than finding the right medication, which can be more speedy. Thus, your patience is going to be tested even more and that's a decision you have to be willing and ready to make.
I take it from the fact that he has to masturbate himself that even if you are masturbating him or engaging in oral sex it is too much emotional stress for him and he loses focus on the pleasure. This seems to be the pattern for him in losing focus: the involvement of another human being causes him emotional distress.
The key, then, is to slowly lessen the distress by getting him to agree to stages of success. Here's what I mean:
You write that he's very goal oriented in sex. This is most likely because being goal oriented is a way to deal with the emotional stress of the whole event of sex with another person. Therefore, the work we're initiating here is to make smaller goals. To get him to drop goals altogether will probably be too intimidating and distressing. So you are going to try to establish with him smaller goals: maintaining an erection long enough to enter your vagina. Then to extend that to long enough to kiss and hug with his penis inside of you. Etc.
Even before that, or with that, might be small goals such as to have you masturbate him for a certain number of minutes without him losing focus before he gives up and switches toward pleasuring you. Goals such as these.
Clearly, working with a psychologist is a good therapeutic model for him. But he needs to now extend that work in therapy to deal with his anxiety and distress at having sex with a partner. A goal may be to have him feel comfortable enough to have you come to session with him to discuss intimacy with his psychologist.
Another possibility is that you seek a psychologist or psychotherapist who is certified as a sex therapist as well. Here is the UK organization's therapist directory:
Given our understanding of this as a psychological problem, he is clearly very sensitive and perhaps even traumatized emotionally. So you have to try to do these things and make these efforts gently and gradually. But it sounds from what you write that you are well aware of this and are a very gentle and loving person yourself.
Okay, I wish you the very best!
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