Why is it important to have compassion for yourself and all others?

Because if you hate yourself and all others it is only a small step to kill all others and yourself. So, at the very least you will tend to die young, crazy and paranoid at the very least if you don't learn to develop compassion for yourself and all others.

Learning that self hate usually comes from negative conditioning by elders and siblings and (friends?) is a good place to start.

Then understanding that as long as you hate yourself your life cannot go very far and as long as you hate others (you just might be goaded into killing others at some point) which may also cause the end of your life as their relatives find you and kill you eventually too.

This is karma in action.

So, it is in your enlightened self interests not to harm yourself or others. It doesn't matter that others have conditioned you negatively. If you are a young adult or adult now you can recondition yourself and your mind and brain in a better, new direction.

However, you have to start by realizing you were brainwashed as an innocent child to think badly of yourself and others.

Another helpful thing is to leave people and friends who are a part of your negative conditioning. You have to let them go in order to become a harmless person who does not harm yourself or others.

It is helpful in this to take Ahimsa Vows which is a vow not to kill anything including insects and to take this seriously.

This has been one of the most powerful vows I ever took around 1983 in my life. Ever since taking Ahimsa vows my life started to become more and more miraculous in every way when I followed my vows not to kill anything including insects.

Even spiders if they will let me I move them alive outside my house where they are allowed to live in the eves of my house or under my deck. However, if I find a brown recluse or Black widow they have to be killed because they are not safe to live around. Also, if I am near rattlesnakes I either have to move them to another place far from people or I have to kill them (one or the other), especially GReen Mohave Rattlesnakes which are little Green sidewinders that are nine times more powerful venom wise than diamond back rattlers in the Mohave desert.

So, in this way you are kind to all the beings it is practical to be kind to and you help the world ecology by not killing anything you absolutely don't have to.

Because all creatures have a purpose here on earth and for earth to be in balance they all need to be here alive.