Because CRB checks operate on a "guilty until proved innocent" basis, which is contrary to the values which Britain has upheld for so many centuries.
These checks are ridiculous anyway, as anyone has the opportunity of commiting a crime the day after they have received clearance.
Also, children are put at more risk when would-be volunteers are put off running organisations or helping with school outings etc. because of the CRB process they would have to undergo. This means that children miss out on vital experiences and/or are left to play in the streets, as they have nowhere to go.
We all want children to be safe but the world is not a perfect place and these checks will not stop the small minority of real criminals obtaining clearance (as has already been proved at a nursery in Devon, for example).
Nor do we want children to be suspicious of every adult they meet, as this does no favours to community cohesion.