I think he's being really shoddy, but I also think your email was too focused on your feelings. This isn't ultimately about feelings. It's a practical, business issue and he is not being professional. I have zero sympathy with anyone who feels defensive when they are called on unprofessional behaviour.

I'm in the UK, so I don't understand this stuff about Ts being late submitting bills. He's running a business, he should act like it.

Stop saying you're being ridiculous. You're not. And stop trying to read his mind, or predict how he'd behave with another client, instead of making your very strong case! I would follow it up with another email along these lines - feel free to cut and paste any of it that's useful but make sure you fill in the gaps where relevant.

Dear T,

I am writing about a serious issue that is currently compromising my therapy with you. As I have explained, my insurance company will reimburse me for our sessions if, and only if, I provide invoices from you. Despite repeated conversations about this, and despite your assurances that you would send me this information, no invoices have been forthcoming. As a result, I am unable to claim back the $xxx I have spent since xx date. We first discussed this at the beginning of June. Over a month has now passed since you told me you would email me the information, and you still haven't sent it.

This is jeopardising my ability to continue in therapy with you. I cannot afford to keep paying for sessions without being reimbursed, and it is not reasonable to expect me to do so instead of using the insurance benefits available to me. It is also jeopardising our therapeutic alliance, as I do not understand why you have delayed sending me the information for so long. A key element of your role as my therapist is to model positive behaviour in terms of self-care and relationships. You have not offered any explanation as to the delay. I have made it as easy as possible for you to supply the information, but you still have not done so. I do not feel this is a reasonable way to treat any business contact, least of all a psychotherapy client.

As it stands, you have gone on summer vacation having still not given me the paperwork I need, leaving me unable to claim back the $xxx. I feel you are not showing me basic courtesy. If we are to continue working together, this has to change. It simply isn't reasonable to expect me to wait this long for the paperwork. I respectfully ask that you inform me of any obstacles to providing it so they can be addressed, and that you send it to me at your earliest convenience. I simply cannot keep spending money on sessions without being able to claim it back. Providing the required paperwork is surely preferable to losing a client. I am concerned that you are willing to leave me in this position, and I really think it's time the matter was resolved.