ESPN anchor Stuart Scott recently died of cancer. In accepting the Jimmy V award for perseverance (in 2014, IIRC), Scott said, “When you die, it does not mean that you lose to cancer. You beat cancer by how you live, why you live, and in the manner in which you live.”
I think that this perspective holds for your question, too. We all die – in a sense, some might think that we all ‘lose’ to the physical imperfections of our bodies. For someone who sees things this way – especially if they believe that this human life on earth is all we have – then suffering isn’t just an evil, it’s the ultimate evil, and therefore, it is to be avoided at all costs.
However, as Catholic Christians, we see that our life on earth isn’t the end-all and be-all of existence. That being the case, the way we live our lives is more important than the brute facts that are printed in our obituaries. Instead, we give glory to God “by how you live, why you live, and in the manner in which you live,” as Scott asserted.
The baby who lives a short life – even if it’s a life that includes pain – nevertheless lives. He experiences the love of parents. He is a living, thinking human being whose life has value. And just as we cannot simply euthanize those who have terminal illnesses, neither can we deprive babies of their lives. (It’s a noble opinion your friend has, of course. He simply wants to reduce pain, and that, in itself, is a good thing. However, we cannot throw the baby out with the bathwater, so to speak: we cannot achieve ‘the elimination of pain’ by murdering a person.)