First of all, there is evidence that children given these drugs for precocious puberty have been damaged by them.
Lupron, used to halt puberty in children, may cause lasting health problems
Why is it that people feel it necessary to stop puberty from happening when a young person may not be 'ready' for puberty
The normal minimum age for puberty to start is 8 in girls and 9 in boys. The children with precocious puberty who are 'not ready' for puberty are younger than this. It's not just that they are not 'ready' for puberty at younger ages, although obviously they aren't, but that a child stops growing after puberty, so these children would end up as extremely short adults if their puberty wasn't delayed. This is a medical condition which requires medical intervention.
but feel it's against nature when a young person may feel that going through puberty at all will be detrimental to their health and wellbeing?
A young person 'feeling' that going through puberty at all will be detrimental to their health and wellbeing doesn't have a medical condition which requires medical intervention. At least not this sort of medical intervention. They may need psychological treatment to deal with their feelings, but they don't need to be given powerful drugs which affect their hormones and have harmful side effects.
Edited for typos.