He arrived with 700 of glucose and from that day on the vets have been able to get him down to 400, 300, 150, but then all the way down to 50, 80 and spiking from 400 to 80 and so on. [...] he was very sad, hardly moving and he looked really really sick. However, today [...] he looked like before, he was rubbing his head against me, giving me kisses and generally letting me cuddle him, walking around and stuff. So I decided to wait again, but my vets tell me there's nothing to do.
I'm so glad your kitty has you to love him and fight for him. I'm very sorry that you have a vet who wants to give up but it is your kitty and your decision. The first vet I took my cat to completely missed the diabetes and refused my request to do any diagnostics whatsoever. Thankfully I found FDMB and from what I learned here I was able to go back to a different vet and get her the help and treatment she needed. FDMB helped me save my cat's life.
What you describe about how your cat is behaving is essentially the same as I saw in my cat when she first started treatment. She was really lethargic and unwell for several days when she first started getting insulin but on the sixth day - and after three days in hospital - she became more alert; more herself. As her body started getting used to the insulin she she brightened up, started scent marking again (rubbing her face against the sides of her kennel) and started to be affectionate again. Progress was slow and steady at first but she kept getting better. Very, very shortly after starting insulin she started eating, drinking and peeing normally again. As her treatment continued she regained the weight she lost, her energy and behaviour returned to normal and her coat became thick, black and soft again. Four months after starting treatment she looked like she had been drinking at the Fountain of Youth (our new vet was
stunned at her improvement). Shortly after that she was climbing trees!
Regulation doesn't happen overnight. Your vet can't "force" the BG back to a healthy range in a few days. The idea is to start at a SAFE insulin dose (enough to start helping the cat to use glucose properly again), test blood glucose and ketone levels (just like a human does - we can help you learn how to test) and then make small, gradual, steady changes to the insulin dose based on the individual cat's response so as to ease the cat into healthier blood glucose numbers while minimising the 'overreaction' and wild swings. As we often say here, it's more of a marathon than a sprint.

The body needs time to 'learn' to be in a healthy blood glucose range again.
But it takes time for the body to get used to the insulin.
If your cat is going down as low as 50 it is possible that your vet is giving too much insulin too fast. As Bron says above, if numbers go too low too fast the body overreacts to protect itself. If your cat's blood glucose is going from 50 to 400 shortly after the wild swings in blood glucose level are very likely a lot of what might be making him feel somewhat unwell on his current insulin dose. Human diabetics who experience big BG swings like that also report that it makes them feel unwell. If your cat is going as low as 50 as measured on an animal glucometer then the dose is definitely too high. Sometimes vets give too high a starting dose and that is what can make the wide BG swings worse, as well as putting the cat at risk of a hypo.
Please can you let us know ASAP:
1. How much your cat weighs (approximately) and whether he is still underweight.
2. The type of insulin he is receiving.
3. The dose of insulin he is receiving.
4. Whether your kitty ever tested positive for ketones. (MAKE SURE THE VET TESTS FOR KETONES!!!)
If you can get this information to us then we can at the very least give you a bit of guidance on what your kitty's starting dose should be as the starting dose is typically based on the cat's weight, not their starting BG levels (assuming no ketones).
Sending lots of positive vibes to little Taro and a
huge 
to you for loving and fighting for him. Diabetes
IS do-able. We'll do everything we can to help you both.
Mogs
.