A lot of black people arrived in Europe comparatively recently, the last ~60 years or so, and often from a specific country rather than the vague concept of "my ancestors several hundred years ago came from somewhere in Africa, but who knows where exactly?"

Besides, not all forms of slavery are equal; what made American slavery fairly unique is that you were born in to it, was for life, based on skin colour, and was an important part of society/the economy.

While the general concept of slavery goes back to before history, this particular combination is actually fairly rare as far as I know. In modern Europe slavery was never part of society in the same way (i.e. you didn't have a slaves in England or Belgium, just the colonies), and in more ancient times slavery was a lot more "flexible" (detail differ greatly) compared to US slavery, in some cases being a temporary thing as punishment or crimes etc.