He went for an operation to save him and it wasn't possible so then they felt the opposite.
Sorry to be pedantic, but it's important.
He was moved to another hospital to be assessed to determine IF an operation MIGHT be a suitable treatment option for his injuries.
It was found this operation would have no positive impact wrt his prognosis, but it was right to explore every possible option and if this had not happened, the parents would have had every right to feel their child had been failed by the NHS.
Compared to other cases, Archie's prognosis was indisputably dire and the case did not offer any legitimate medical challenge to that fact.
This case was fundamentally about a family who (for reasons we don't really understand and it's thus pointless to speculate on) could not/would not accept that Archie had died on the day (by intent or misadventure) he was sadly found by his mother having hung himself.
It furthermore (despite Lidell's ridiculous article) underscored the principle that the patients best interests are paramount, even when they conflict with the wishes or best interests of the family. Which is exactly how it should be.
Deviation from that principle (even to be kind) sets a very dangerous precedent and Liddell fundamentally asked the wrong question. It wasn't "what's the harm" in moving Archie, rather it was what was the benefit to him?