Sorry maybe someone has said this and I missed it, but it seems to me that your childless cousin was relating that her friend was having a great time and you did an all-knowing "ah but it's actually REALLY hard" patronising bit and she snapped at you, perhaps because, well, she doesn't want to think of all the downsides all the time.
My grandmother told my mother as soon as she got pregnant not to listen to the horror stories other women tell you, that some women will do anything to highlight every negative aspect of being a mother to frighten you when you haven't been there yourself.
I found early motherhood absolutely amazing, absorbing, awe-inspiring, shocking if occasionally terrifying and overwhelming. It was unbelievable but also incredibly intimate and personal. Even now, only a mere two years later, even the hardest parts of it seem precious and make me ache for the transience of it all.
I don't think anyone can explain it to anyone else, and I often think that in trying, it very quickly sounds like whinging, moaning and competitive misery. I don't think that saying it's great is lying, I thought it was even though there were moments I sat over my newborn and sobbed because I hadn't a clue what I was doing. I think that's great, others think it's the worst experience of their life. It's individual, like everything else.