This is an interesting post Uhura.
I am a dictionary hound so I had to look up agape in the wikipedia
In this respect, I have come to observe in my own life and the interaction with others that agape love is very rare among anyone, blood relative or other. There is generally many conditions placed on loving each other. Many expectations placed on children from their parents to be certain ways, display certain behaviors, etc...
I think as we grow through trial and tribulations, and heartbreaks and all that life throws at us, we become more open, we become more like the flower that is blossoming, we either become more open or not...to loving what is. Which brings us closer to "agape" love. Some humans open and some do not as they grow older, this can be observed among the elderly, some grow bitter and angry and others are smiling and laughing and enjoying life even as they are strolled around unable to walk on their own any longer!
I think what we experience with our children is something else, some hormonal effect to care for and nurture our cubs, which either occurs during birth, or occurs as we realize that this innocent child is unable to get their own needs met alone and thus we something, possibly hormonal kicks in and we step into that role and instinctively we are able to become bonded or become parent like to another child. I have noticed there were times when I felt that kick in even towards an adult, where I perhaps over stepped into thinking they needed this or that as though I were their parent. LOL!
To me, unconditional love is simply loving what is...no matter what. Not longing for more or for something to be different, just simply loving the way it is in the present moment, no matter what that is. I totally believe we are all capable of that, but I also think that our society at least in America does not support this notion very well if at all, so we have been conditioned to judgments about practically everything. There is always a right and a wrong way or type of behavior, noticed and expounded upon so we become judger's and condemners-which in my understanding and my own judgment doesn't equal agape or unconditional love.
Thank you for bringing this up, I am going to begin my day thinking about and having an awareness of the present moment and loving what is today!