If children are "a gift not a right", that should be applied equally to fertile couples too. It makes no sense as an anti-IVF statement, as of course children born through IVF are just as much of a gift.
If the answer to not yet being a parent is "why don't you just adopt?" this should be equally recommended to fertile couples, every time they mention their hopes of having a family.
If we "ought" to think about "all the children in care who need a loving home", then that applies equally to those with or without fertility problems.
If a couple can't afford IVF, it doesn't mean they can't afford to raise a child, because of course an amount phased over 18 years is very different to suddenly having to lay your hands on several thousand immediately.
If it's not OK to pass on genes which could affect fertility, the same should apply equally to all other genes which may cause problems (obviously a dreadful idea, and the real answer is to allow couples their own choice). Additionally, many causes of infertility aren't genetic or have a low risk of being passed on.
If IVF is solely responsible for the lack of funds available for cancer treatment, then so are the staggering percentage of A&E attendances which are related to alcohol, every missed GP appointment, the multi-layered beaurocracy, treatments for things which make far less of a difference to someone's life than IVF, and dozens of other factors.
If treating a woman for medical difficulties with her reproductive system is subject to NHS cuts, then the same should apply for treatments for the male reproductive system.
Why should anyone but the woman herself decide whether she wishes to go through what IVF entails? Particularly as she is clearly very willing to give birth several months down the line, and no Robert Winston is going to prevent her.
If "get a dog/cat" is the answer to fertility problems, then all the fertile people who blithely suggest it are presumably happy to have their own family supplanted with a dog/cat.
If "everything happens for a reason" why do some potentially fantastic parents never have the good fortune to have children, unless the "reason" is random chance?
If the world is overpopulated, that clearly isn't due to infertile people but the opposite, so it's illogical to deny people IVF on that basis.