It's not that life is unique because as you have correctly stated, it repeats itself, but rather a person is unique in their life experiences.
The experience is new to a person or it has something different than the one prior. Life's lessons are presented again and again until you learn the lesson.
Sometimes I forget that when an authority figure is wrong, no matter how right I may be, I shouldn't open my mouth because most people don't want to be corrected no matter how nice I try to say what I have to say or even if I do it in private.
The person is unique in how he/she handles the experience and what is learned from it.
The lesson for me, "Keep my mouth shut" and let the person lesson the way I've learned mine with experience.