Ever notice the difference between Happy and Mad?
It's so simple, really... and yet profound.
To start with, in much the same way as "Love," these are primarily referred to as states of mind, but are also
verbs. You might say "So and so (is) Mad at" in much the same way as you'd say "So and so threw (object) at" or "So and so was running at." This is a forceful verb. Happy is more easily grammatically pleasing; the phrase "person is happy with person two" is directly correlated to a phrase like "person is shopping with person two." Happy is a gentle verb.
But the clearest difference is the usage of "at" and "with." You cannot say "mad with" any more than you can say "happy at." Not only do these particular unique qualifiers
sound right, but they tell you more about the verbs. At infers that one object is being spoken of. At is a solitary word, and "mad at" is polarizing... one person can be mad at another, but the other person does not have to be affected by the angriness of the first. With immediately tells you that two objects/persons are being unified. "Happy with" works in grammar and in real life because when one person is happy, in the majority of cases that happiness is contagious, especially if the happiness is directed at someone in specific.
So... more scientific/oddball then profound... but i thought it was an interesting concept.