This "slippery slope" could eventually lead to an increase in women having babies in their 60s, she said.
"Increasingly we are seeing women in their 60s approaching clinics to have children," Dr Zweifel added. "The studies suggest it is traumatic for a child to lose a parent at a young age. Additionally the emotional impact of being a caregiver to an ageing adult can be devastating.
'If you are a teenager you are not developmentally prepared to deal with that anguish or responsibility."
In the UK, there has been a steady increase in the number of babies born to older mothers in the last 15 years.
Although there is no legal age limit for patients seeking fertility care, most clinics will not treat women over 44 with their own eggs or women over 54 with donor eggs.
According to the Office for National Statistics, women aged 45-49 had 705 babies in 2001, rising to 2048 in 2016.
The 50-54 year olds had 53 babies 2001 rising to 218 in 2016.
In those over 55, there were two babies born in 2001 and 20 in 2016.
The US has seen a similar trend.
In 1996, there were 3,045 births to women aged 45-49 but by 2016 this had risen to 8,257.
In 1997 there were just 144 babies born to women aged 50-54 but this increased to 786 in 2016.
Dr Julia Woodward, Director of Psychological Services at Duke Fertility Center in North Carolina, co-chaired an ASRM training session with Dr Zweifel for 100 medics who wanted guidance on dealing with older fertility patients.
She said older couples were the one patient group who kept her awake at night with worry.
"I am worried about the woman during the pregnancy, her risks of post partum depression," she said. "And what is it like going through menopause with a preschooler? What is it like to be enforcing a midnight curfew for your high school senior when you are pushing 70? What is it like for that child who is having to alter and delay their own life plans. They cannot backpack across Europe this summer because they are going to want to stay home and get mum through that hip replacement."
She said studies showed that children of older parents worry about them dying and finding their bodies, were embarrassed by their age and upset they would have fewer years with their parents alive.
Parents also faced significant challenges. Not only were they exhausted looking after a newborn, but later on they felt they could not fit in with younger mothers because of their age. They were also upset when they were mistaken for a grandparent.
Dr Woodward said women in their 50s seeking treatment often felt younger than they were and wanted to copy the lifestyle choices of women in their late 30s or early 40s even though they are in their 50s.
The oldest woman to have a baby in the UK is Elizabeth Adeney from Suffolk, who gave birth to a son, Jolyon, at the age of 66 in 2009. At the time she said it was not her age that mattered but how she felt inside.
Professor Geeta Nargund, medical director of Create Fertility in the UK, said: 'We know women are leaving it late to have children in Britain too and reproductive tourism for older women to go abroad for donor eggs and come back pregnant is increasing.
'I think the number of women in their fifties doing this will rise even further and it can cost the NHS hundreds of thousands of pounds to deal with pregnancy and neonatal complications such as miscarriages, pre-eclampsia, multiple births and stillbirth in these women.
'The older fathers linked to these women also have children with a greater risk of autism and psychiatric difficulties.'
She added: 'Children and teenagers need their parents to look after them, not the other way around.'
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