My understanding is that what Martin Luther King means by strong demanding love is love that is compassionate and genuine.  This kind of love is an expression of one's truth and integrity.  This kind of love is based on seeing myself and the other as one, no one better or worse, higher or lower than than other.  With this love the other is seen and respected as equal.  This kind of love puts the golden rule into action and I treat others as I want to be treated.  This kind of love is not a superficial and transient infatuation or passing fancy, but a life commitment and posture.  It is strong and demanding.  Emotion may be involved in this kind of love, but it is deeper than just emotion, deeper than thinking, deeper than physical -- it comes from the soul.  An experience of such love has been when I have spoken or acted with pure and total integrity independent of what others think or say.  Honestly evaluating my motives in what I say and do helps me check whether my action is filled with such love.  If I have an agenda or intention that I am trying to accomplish, it's time for me to be suspicious of what I am up to as the pureness of my love is likely diminished.