Now you, on the other hand, are the liar. You claim that all life is of value yet you would allow for the killing of a born alive child.
I would - and I value life. Those two things are not incompatible. I said that I would accept euthanasia for a person who is unconscious and is not expected to ever recover. That is if they are two hours old, two years old, twenty years old, or eighty two years old, or any other reasonable age of existence. It is about whether or not they will ever have a life. Not a "good enough" life, or an intelligent life, or a life where they have enough money, or a life where they are not an inconvenience to their mom, or any other arbitrary and idiotic reason that a mother can choose to kill their child. This is about whether or not they will experience life, and it is up to the family involved. This is far more true for a person who chooses and expresses they would like to have the plug pulled (colloquially speaking) if they are ever in such a position than for an infant, but I do believe a respectful euthanasia is better than starting and living life as a soulless vegetable.
You may find that the same thing as "my boyfriend doesn't want me to get stretch marks, so I'm going to kill my baby" or "I never wanted to be a mother, and I want to be able to afford college, so I'm going to kill my baby" or "oh, my goodness, this is a girl and I wanted a boy, so I'm going to kill my baby" or "Downs Syndrome is no way to go through life so I'm going to kill my baby." All of those "convenience of the mother" reasons are NOT reasons to allow euthanasia. That you can't see the difference is really on you, not on my position.