Back in my younger days as a Greek worshiper, I used to worry a lot about if I had possibly angered the Gods, so I am not so naive as to think that I am the only one. Thankfully, my mind is at peace with this, due to my realization that the immense goodness and highness of the Gods, makes it impossible for them to be subjected to human actions. In other words, beings which are inferior to the Gods (humans), cannot possibly possess the power to change the mood of those who are not inferior (Gods). In fact, some might consider it to be disrespectful to suggest that we can, in fact, control the mood of the Gods.
When you are talking about Gods, you are speaking of beings who are above anything humans can do. This also means they are above our minds and emotions. Simply put, you can't make a God mad because you don't have the power to change them. Angering the Gods is a concept most appropriate for myth and people who are paranoid of being punished (superstitious). That is not, however, to say that the Gods do not send justice. They most certainly do, and that varies from situation to situation, but this is not the same as anger. Also, being that the Gods have known us for centuries, I would say that it would only seem logical to me that they understand us. They know how we think, they know our emotions, and they know why we do the things we do. Knowing this, the Gods understand that it is only to be expected that we will falter and make mistakes. And yet, they remain, wanting to take part in our lives, and help us along the way. Compassion, understanding, and obviously, extreme patience do the Gods have, and when one has these things, anger and the determination to harm cannot be present, because such things are the opposite.
In conclusion, we can't anger the Gods because, one, we can't change them. And two, because they expect us to make mistakes because that's our nature. One does not get angry at someone or something for doing what it does naturally. You don't get mad at a lion for roaring, or at a bird for flying, and you don't get mad at humans for making mistakes. By not running and hiding, but instead acknowledging them when they happen in our lives, we can purify ourselves of the error and do better in the future. Always remember that each day is a chance to be better than the previous.
In the Goodness of the Gods,
Chris.