There are very good counter arguments you can easily find online.
I'll give you my favorites.
For intellectual property, it is not real property. Property is the category of things that are material and can exchange hands. Data, like speech, does not get literally exchanged, but copied. So there's no such thing as intellectual property.
Imagine you can memorize whole books. Would that be illegal? What if your friends could phone you and ask you to recite some paragraphs from memory, would that be illegal? What if you were part of a group of people that memorized the books they own and they ask each other to recite over the phone one page a day from a book they don't have? A hard-drive is a shortcut for that brain capacity we don't yet have. But if we did have that capacity to memorize, it would not be illegal. So instead of enjoying hard-drives to freely books and songs, we are criminalizing an arbitrary human enhancement.
For child pornography, I find it hard to justify the suppression of criminal evidence. We all should fear a government that has the power to arrest someone and suppress the evidence for their crime. If someone kills someone else even if just to film it, that would be a crime (or many crimes) but the video should not be illegal to possess. Evidence of gruesome deaths (intentional or not) are likewise legal to possess. What should be illegal is the act in itself, not the documentation with which we prove the crime.