Chris Gard and Connie Yates became upset and left court, when the judge said it was "absurd" that a dispute over 11 month old Charlie's head size was "undermining" the case.
His parents' lawyer told the High Court Charlie's mother had regularly measured her son's head and disagreed with the hospital's measurements.
The court heard Ms Yates had measured her baby's head on Thursday morning and there was a 2cm difference with the hospital's measurements.
Doctors have said the baby's skull has not grown in three months, which suggests a lack of brain function.
Roger Kiska who is part of the Legal Council team at Christian Concern told Premier the courts should respect the rights of Charlie's parents.
He said: "Across the board there should be respect for parental rights and rightfully so because it is the parents who are best placed to make these decisions - they're the ones who loved their child the most.
"What you have really basically is a cold hospital bureaucracy - the hospital is a great hospital but the reality is they're not as personally invested in Charlie as the parents are and we're hoping that the court recognises this fact."
Charlie's parent's lawyers are hoping a High Court judge will allow Charlie - who is on life support at Great Ormond Street Hospital - to have the therapy, but British doctors don't think it'll improve his condition.
Before the hearing, family spokesperson Alasdair Seton-Marsden read out an emotional statement from Charlie's mum and dad.
He read: "We love him more than life itself. If he is still fighting, then we are still fighting."
Mr Justice Francis has ordered for an independent person to measure Charlie's head within 24 hours.
Kiska disagreed with critics who have said Charlie should die with dignity and said society is wrongly defining what dignity means.
He said people should be "supporting life" and "supporting caring - not killing".
Speaking about the courts he added: "We're hoping that they see that removing hydration, removing nutrition is bringing about an unnatural death perhaps and this in a sense is de-facto euthanasia as well."
Meanwhile, an American doctor offering to treat Charlie Gard says new data has emerged in the three months since a judge decided that the terminally ill baby should be allowed to die with dignity. The doctor on Thursday told a High Court hearing in London that he thought treatment would be worth trying.
Listen to Roger Kiska speaking with Premier's Glen Thompsett:
