Everyone, everyone has the right to be happy
Do you want to know something embarrassing? That makes me cringe when I think about it? It's that the following quote was the hardest thing for me to stomach about Buddhist philosophy thus far:

"Whether people are beautiful or plain, friendly or cruel, ultimately they are human beings, just like oneself. Like oneself, they want happiness and do not want suffering. Furthermore, their right to overcome suffering and to be happy is equal to one's own. Now, when you recognize that all beings are equal in both their desire for happiness and their right to obtain it, you automatically feel empathy and closeness for them. Through accustoming your mind to this sense of universal altruism, you develop a feeling of responsibility for others; you wish to help them actively overcome their problems. This wish is not selective; it applies equally to all beings. As long as they experience pleasure and pain just as you do, there is no logical basis to discriminate between them or to alter your concern for them if they behave negatively." (Tenzin Gyatso, the Fourteenth Dalai Lama, The Compassionate Life, 22)

There have been people who have hurt me deeply. (Who hasn't? And then there are always public figures that you might hold a deep-seated antipathy for.) I could not bring myself to accept that they, who caused me such pain and misery, could have an equal desire, claim, and right to the happiness I imagine I do. How is that fair? Shouldn't they be miserable, because they made me miserable? Shouldn't they hurt, because they hurt me?

2 Nephi 2:27 (a scripture in the Book of Mormon) says that the devil "seeketh that all men might be miserable like unto himself." And then there is of course the quote famously attributed to Gandhi: "An eye for an eye ends in making everyone blind." So, to harbor such deep-seated anger, bitterness, and resentment that I would deny the right or ability of anyone to be happy is ultimately, completely destructive and actually puts me right in cahoots with the devil himself.

Holy crap.

Ok, so that is the negative side of my breakthrough/acceptance of this idea. Now, another passage from the Dalai Lama, restating the positive side of subscribing to the idea of universal altruism and of seeing that we are all, essentially, exactly the same:

"We all share an identical need for love and on the basis of this commonality, it is possible to feel that anybody we meet, in whatever circumstances, is a brother or sister. No matter how new the face or how different the dress or behavior, there is no significant difference between us and other people. It is foolish to dwell on external differences because our basic natures are the same.
The benefits of transcending such superficial differences become clear when we look at our global situation. Ultimately humanity is one, and this small planet is our only home. If we are to protect this home of ours, each of us needs to experience a vivid sense of universal altruism and compassion. It is only this feeling that can remove the self-centered motives that cause people to deceive and misuse one another. If you have a sincere and open heart, you naturally feel self-worth and confidence, and there is no need to be fearful of others." (The Compassionate Life, 37-38)

To understand those who cause harm

There's also a passage in this same book that introduced to me a skillful way of thinking about/understanding people who cause you harm, a way clear of anger, hate, or bitterness, because you focus on the basic nature of the person, which is identical to yours:

"You can also reflect on how, if it is the essential nature of the person who is harming you to inflict harm on others, there is no point in being angry, since there would be nothing that you or that person could do to change their essential nature. If it were truly the person's nature to inflict harm, the person would simply be unable to act otherwise. As stated by Shantideva:

Even if it were the nature of the childish
To cause harm to other beings,
It would still be incorrect to be angry with them.
For this would be like begrudging fire for having the nature to burn (6:39)

On the other hand, if harming is not the person's essential nature, but instead their apparently harmful character is merely incidental and circumstantial, then there is still no need to feel angry toward that person since the problem is entirely due to certain immediate conditions and circumstances. For example, he may have lost his temper and acted badly, even though he did not really mean to hurt you. It is possible to think along these lines as well." (81-82)

Matthew 5:44, Jesus told us to "love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you."

The Buddha said, "Hatred does not cease by hatred, but only by love; this is an eternal rule."

Lovingkindness: Loving self, neighbor, and God

So, universal altruism is not only necessary, it is absolutely possible. The metta, or lovingkindness, meditation goes like this: (I think ideally you're supposed to repeat it as you meditate...that's what I do, but I'm a newbie :) ):

May I be peaceful.
May I be happy.
May I be well.
May I be safe.
May I be free from suffering.

May all beings be peaceful.
May all beings be happy.
May all beings be well.
May all beings be safe.
May all beings be free from suffering.

It's such a beautiful meditation. You start by nurturing and loving yourself, which can sometimes be as hard or harder than nurturing and loving others, but is just as essential. You cannot disregard your own right to peace, happiness, and well-being and expect to be able to nurture others. From there, from nurturing yourself, you expand and project lovingkindness to encompass all beings. It's deeply interconnecting.

This metta meditation is, to my Christian sensibilities, a beautiful application of the scripture from Luke 10:27: "Thou shalt love the Lord thy God with all the heart, and with all thy soul, and will all thy strength, and with all thy mind; and thy neighbor as thyself." I love that self, neighbor, and God are all in the same verse/commandment. Because, when you think about it, when you "touch deeply" the nature of God, self, and neighbor, you see that we're all the same thing, really. If I understand correctly, this is what Thich Nhat Hanh calls "interbeing." He uses the analogy of water and waves: We're all waves, and at the same time we're all at our core the water that constitutes us. To love a wave is to love the water; to love the water is to love the wave. God is our basis of existence; God is the water. We and our neighbors are the waves. To love neighbor is to love God and self; to love God is to love neighbor and self; to love self (not in a corrupted, selfish way, but in the same nurturing way that you love God and neighbor) is to love God and neighbor. Because we're all the same stuff: We're all children of God, and as such, share Him as our foundation of being.