I won't say every child of divorce feels this way. I can't speak for all of us. I do know this is how I feel, even now after 30 years since my parents' divorce.
It hurts knowing that two people who created me, whose nature and nurture both influenced me, hate so very much the parts of me that are the other parent. It hurts knowing I can never been 100% loved, because I will always be, however partially, someone hated.
I share this not to change anything in my own family. Decades of history have pretty much solidified its dysfunction. I share this as a cautionary tale. Before you open your mouth, slit your eyes, purse your lips or otherwise show your derision about your co-parent, consider what your children are internalizing. Then consider again, because I guarantee they're internalizing more than you could ever imagine.