Because it is the American dream that one day - through hard work and determination - you can become one of the privileged. As such, any attack on the privileged is an attack on future you - or at least the future you that you hope will one day exist. Of course the irony is that the more you protect the privileged, the more you end up preventing future you from ever joining those ranks.
The existing privileged understand this perfectly, which is why they craft their message the way they do, bathed in apple pie and American flags, framing everything as an attack on your rights. And so we Americans rally forth against those who would dare try and take away that which isn't but might one day be ours. And in the end, the privileged become more privileged, and point to the rest of us and say "this is what the people want."
And we the people pat ourselves on the back for a job well done, because though we just made it harder on ourselves, at least our American dream is still intact.