Perhaps it can be expressed in acorn form first, but there is a large and complex tree buried in this insight, which will take a lot of room to fully express. To start, we have this realization that is predicated in a sense of survival, a sense of continuity. Whether it arises in reaction to a horror of death or is something deeper and kinder, for example a thread connecting us to All, is not so important as the realization that we each have within us a powerful motive to stay alive.
So accepting that as a foundation, we can look into the future and realize that after we eventually die all that remains are the memories others have of us -- and a few odds and ends which shortly belong to others. Once that fades, for the average person there is little left but a faint ghost imprint upon eternity of a fleeting blink of an eye that constituted the life of one among many, roughly as consequential as the life of an average ant 500 years ago.
For a great historical character, one whose life and decisions shaped a generation or more, it's different, and the fading with time takes much longer. Consider, for example, Isaiah, or Shakespeare, or Julius Caesar, whose life works still live on, reverberating down through the centuries, dying and resurrecting many times as different ages review their work. If one of the attributes of deep time is to erode all individuality and generalize each tiny moment of time into a more abstract theme being communicated from one end of time to the other, all that remains in the end is a state which, from our perspective, seems to be better than the beginning, with lots of long-forgotten tales woven into the tapestry between. (Maybe not long-forgotten; maybe the end carries an accurate summary of all that went before, and each moment between the two endpoints can be drawn out of the end and inspected, even as it could be predicted -- perhaps in principle only -- from the beginning.)
All of this is to say, there is a sort of moral imperative which operates with only minor reflection: "If I am to live at all, I must continue living. If I am to continue, I must make peace with those forces over which I have no control, which could extinguish my little candle flame. Even my own children grow to become that over which I have little or no control, even they may grow to become a force which could bring about my end before the 72 years allotted. Hence it is in my best interest to be as kind, thoughtful, and forward-thinking as possible with my own children, in order that they can both live in a way that keeps me alive, or at least does not threaten my existence, and in a way that perpetuates their own lives, for at the very least they are carriers of memories of me." Admittedly, this is a selfish line of thinking, but this is a rough draft, and it seems coherent enough and general enough across all living organisms, that we should be able to draw a type of Law of Nature out of it. (Hopefully something a little more elegant than "survival of the fittest" but in a pinch that will do.) Continuing the thought, though, we see that the best way to teach any principle is to model it somehow, and to model this reasoning, we must therefore be kind, thoughtful, and forward-thinking as possible to our own parents, for if we expect something of our children which we do not give to our parents, there is a basic inconsistency that makes reasoning fall apart.
I'm in a hurry. There is actually much more, further I wanted to go with this thought, but time is now short due to a bus I must catch and I have captured this point clearly enough, so some other time, I'll pick up the related link to a developing argument for the existence of God which is that the existence of everything is proof that God exists and is good, for otherwise there would be only chaos. Honest, it is related. But enough for now...