I'm interested by this comments about how "having a child is not a right". I agree it isn't a right in the sense that nobody can grant everyone legal rights to something which may not be physically possible.
When we talk about rights we might talk about human rights, such as the right to life, the right to a fair trial, the right to a private and family life, the right to freedom to practise your religion etc. We might also mean things like consumer rights or employment rights which are granted to us by law.
Publicly funded IVF isn't about people's rights to have a child, because sometimes with even the best will in the world, excellent medical care and a bottomless pit of money, it just won't be possible.
Publicly funded IVF is about people's rights to medical care. It is medical care that is aimed at treating a medical problem and thereby improving the patient's quality of life. I don't think there is any great distinction to be made between medical care which treats the cause of the problem and medical care which treats the symptoms. If you mend someone's broken leg, you are treating the cause of the problem, and with good medical care and a straightforward recovery you should be as good as new afterwards. If you give someone medication for chronic arthritis or Parkinson's disease, or if you supply an amputee with a prosthetic limb, you aren't treating the cause of the problem but you are treating the symptoms and helping the patients to live a better quality of life. If you allow an infertile couple to access IVF treatment and they successfully have a baby, you aren't treating the cause of the problem but you are treating the symptoms (childlessness). Looked at in that way, IVF is a better return on investment than treatment for many chronic illnesses because if successful it treats the symptoms permanently. The couple will still be infertile but being fertile only matters if you want to have a baby. There is no need for lifelong medical treatment for the post-IVF couple in the way that there is for people with chronic illnesses, whose symptoms may be alleviated somewhat but will still have to live with their illness for the rest of their lives. In that sense, successful IVF treatment is just as good as mending a broken leg. It may be treating the symptoms rather than the cause of the problem, but it does so so successfully that the cause of the problem is no longer relevant.
So back to rights. If funding for IVF is about a right to healthcare rather than a right to a baby, do we consider that we all have a right to healthcare?
Rights are not fixed in stone. Rights are fluid and vary considerably over time and in different countries. In some countries people have no right to healthcare, and it is only available to those who can afford it. In Northern Ireland women don't have the right to an abortion. In Saudi Arabia women have only just gained the right to drive a car or vote.
Rights are man-made (quite literally "man" made, in a lot of cases) and depend entirely on where and when you live.
So if you believe that in the UK in 2020 everyone has the right to medical care, why should that not include IVF?