You are right that the amout we suffer in life can vary wildly. We all have our stories, our backgrounds, our unique views on the world, and so on. Although I do still believe there is inherent suffering on Earth, the amount each human suffers on a day-to-day basis is different based on an innumerable amount of factors, most of which are beyond our control.
For cooperation: yes, ofcourse there is cooperation in life, especially in human history. But looking at the very fundamental level at which life operates, it's about combating entropy. Staying alive is work. A living organism that does nothing will wither and die eventually. We all need energy, nourishment, and rest. Try to stop sleeping and see where it leads you, or starve yourself intentionally, and you will die. I am talking at the deepest, fundamental level at which life works in our universe. It's a rebellion against entropy, which is fascinating and beautiful in my opinion, but also harsh. Every day, millions (if not billions) of living organisms are killed to nourish others (mostly humans), or they fall ill and succumb early, or miscarriages happen, and so on. There is no inherent justice or karma in life, it is seemingly extremely random, ambivalent, and unfair to human minds. Those who experience suffering first-hand, especially at a young age, typically awaken much earlier to this harsh truth. If your life is all pleasant, easy, and fair, then life seems like paradise. Until your parents pass away, or your best friend silently leaves you, or your partner cheats on you, and then you don't know what to do, because your worldview was shattered.
This is also why creating a genuinely fair, just, and meaningful world is so important. Humans are intelligent, cooperative, adaptive, and creative enough to create a world that is in accordance to our needs, where we genuinely care for each other, we don't discriminate, we don't condone violence or racism, and so on. But we now live in a competitive free-for-all, and it's been absolutely disasterous to our spirit. It is not normal that millions of people suffer from mental illness, or physical health issues like obesity, or the immense loneliness that so many feel, or the disconnect and agitation between the sexes. Why don't we create a world where we are free again: free to love, to be ourselves and to be different, free to create meaningful and beautiful art, and free to explore the wilds again. Why can't we return to our legacy.....
You will only empathize with me if you've also been to this depth of despair. This is not stated out of arrogance, but out of truth. I've been neglected, bullied, rejected, and i've had to deal with illness and loss at a young age. There is no doubt this shaped my worldview and even made me somewhat bitter, although I do my best not to falter to nihilism. But i've experienced the cruelty, apathy, and injustice in our world first-hand, especially since I am 'lower class'. When you view the world from my perspective, everything I've said so far will make sense.
Pain is not suffering but i'd classify it as some part of it. If you injure yourself physically, don't you suffer physically aswell? Pain can be a broad concept but I was mostly referring to literal or physical pain, like injuring yourself in a literal sense.
And for protection: yes, I stated that. We should prevent bullying and protect the most vulnerable in society. However, that is not the same as enabling a victimhood complex or deluding ourselves that life is always fair and nice. We should both teach our children to be kind and empathetic, but also to take control of their own emotional and mental well-being. They are not mutually exclusive.