I have had three male dogs, all rescues, all neutered at different ages for different reasons.
First was a GSD cross rescued from a puppy farm as a pup and highly fear aggressive. This was decades ago and I knew nothing about dog behaviour back then. Bloody awful veterinary behaviourist we saw recommended getting him neutered at 8 months. Worst mistake ever, his aggression and nervousness increased and we ended up having to change our whole lives and move house to make sure he could live a full life and not endanger anyone else.
Second was another large breed, not neutered until he was 8 and then only for medical reasons (prostate and bladder related). No change in behaviour at all, still the same lovely placid dog he always was, but we had to reduce his food intake and he did gain weight more easily afterwards.
Third, also a large breed, rescue tried to force us to neuter at 6 months, my vet refused and wrote a report that the rescue accepted. He was highly anxious, scared of other dogs when they were off the lead and had developed lead reactivity. The rescue tried again to force us, against veterinary and behaviourist advice when he was 1 year old. We fought it, but they threatened to sue us and take him back, so we had no choice, after all the wrangling he was eventually done at 18 months and was anxious, fearful and reactive to other dogs his whole life, despite lots of work and excellent behaviourist input. General consensus was that he was always going to be that way due to poor breeding and a really bad start in life, but that neutering compounded it and made it harder to overcome.
I would never neuter for aggressive behaviour and would definitely follow the science on when/if it should be done. The study PollyRoulllson referred to is really worth a read.
We will be getting our next puppy in a few months (Mum is due any day!) and as it stands, I am not planning to neuter or if I do it won’t be until well after he is fully mature and grown.
As a complete aside, but possibly relevant point, going into menopause myself has made me really think about neutering pets. The loss of my own hormones, by perfectly natural age-appropriate means, has had a really detrimental effect on both my physical and mental wellbeing, including suddenly developing anxiety for no apparent reason, so why would removing the hormones of otherwise healthy happy dogs be any different. I’m still musing this point, but it’s definitely food for thought.
I’m not anti-neutering, I just think it needs to be considered on a case-by-case basis and all the relevant factors properly considered. I totally understand why rescues feel the way they do about it, but for individual owners of non-rescue dogs it needs to be a carefully considered decision and not an assumption that it’s always necessary. As for rescues that threaten to sue when an adopter says they want to delay neutering per advice from both veterinary and specialist behaviourist sources who have been working closely with that particular dog. Well that to me is absolutely bonkers and when policy starts ruling ahead of the welfare of the animals they say they are protecting - especially when they are willing to use their funds to sue the adopter who has spent the last 18 months spending thousands on specialists trying to help the dog.