There's no evidence that transwomen offend at a lower rate than other men.
You could apply your argument to other groups of men. Blind men, gay men, men in wheelchairs. Should they be given the access to women's single sex spaces that transactivists demand for transwomen? If not, why not?
Nobody thinks 11 year old boys are likely to be sex offenders. Do you think all 11 year old boys and girls should change together for PE and swimming? Why not? It's not just about safety is it?
The onus is on you to show why some men are special, not for women to have to endlessly explain why there are no special groups of men.
What about trans men. Are their offending rates any different to other women.*
Are blind women*, women in wheelchairs any different? Should they be given free and unfettered entrance to male only areas. Despite the fact that disabled areas tend to be unisex.
Most living with a disability aren't making demands for extra access to able bodied areas. We're just after equal access. The same is just as likely to apply to any trans woman or trans man. The right to live their life, without having others pointing out that "they shouldn't be allowed in here".
Why are you happy with the fact that a trans man should have unrestricted access to men's areas/groups, and that men, or boys, should have no problems with that. But not willing to even contemplate a trans woman in a women's area/group?
Worth reminding you that Britain's youngest double murderer is female, not male.
Unless there's been drastic changes in recent months, changing areas aren't designed and specified by age. That'd be an extra cost, that would be passed onto the end users.
I would say that the onus is clearly on yourself to prove that there are "special groups of men" in the first place. And does this mean that there are "special groups of women" making similar "demands" as well?
*I'm using this wording simply because you refuse to accept people for what they are. And what the law says.