Unconditional love exists. However, it is rare. I believe my mum loves me unconditionally, and I love her the same way. My father and I do not share that love. Many bonds that I believed were unbreakable have been broken because of some act or lack of action from another. Even the bests of friendships are not unconditonal, since things are expected. When expectations are not met, the bonds of friendship can be strung too tight for it to hold.
Btw, my cats love me too, they tell me every morning, right before they demand food