How to teach sympathy/empathy in Buddhism?

Due to the nature of society there is always a tendency to shape our child and, for many reasons, I think this is only natural. Some parents believe that their child isn't perfect - a subliminal message we get from society, which we pass over to our children. Using society's blueprint for perfection, they will try to mould their child with that blueprint in mind. The issue with this is the child will hear this message, the child will develop an overbearing sense of wrongness about themselves. This is what I call the implicit subscription to neurosis. Some parents will want their child to follow their own ideologies, they will want their child to become a smaller version of themselves, perhaps because of an unconscious fear about endings - seeing their character pass on through another person appeases some of their own anxieties. This can be another form of imparting unconscious anxieties onto the child. Even to teach your child that they are lucky is to teach them a kind of conceit: how to measure themselves against the misfortunes of others and feel good about it. For most, this luck-bearing attitude is a stick-wielding mentality used to prize apart segments of society. This habitual need to create schisms is where your confusion resides, and love & compassion is the resolve of that confusion brought about by wisdom-understanding. In some odd sense, confusion is the stepping back from it all so that we can seek a new perspective. Stepping back gives us a little refuge.

I could go on and on about the parent/child relationship, it goes as deep as the neurosis it rides upon, but let me just offer this rather wide summary:

It is within the entire scope of humanity that we bear the foibles and deficiencies of each other's behaviour and later come to a wise reassurance about its function. This means getting intimate with life, regardless of your level of understanding about things. That level of intimacy eventually coagulates to form empathic understanding. You see, this is beauty in all its glorious forms. It is a beauty that always permeates the warp and weft of human interaction, weaving a grand tapestry for the greater good on a rickety loom we call earth. It may at times appear terrifying, disgusting and bloody wrong. It is during these times that we begin to question its function, and that questioning pushes our attention inwards towards our own perceptions, towards our own wisdom. In the meantime, one just does their best in the world, and afterwards one just does, without dumping our psychological issues on our children.

The Buddhism i follow teaches that all beings are the same and are experiencing results of good and bad actions, also after death, in the next world [an after-life] and that there is no beginning to this transmigation from one world to the next.

It teaches that we inherit the results of our actions, mental, verbal & physical and that others are like ourselves albeit differently conditioned, having different amount of delusion.

What is good for others is good for us because we are all alike.

Therefore if we have sympathy & compassion for ourselves we should develop sympathy & compassion for others.

In this way one embraces all beings with sympathy & compassion and reaps rewards of good mental, verbal & physical actions.

May all beings be happy, may their minds be steadied by virtue, may they make straight what is crooked on a path so hard to walk and be free of all ill.

Have you heard of the four Brahmaviharas (abodes of brahma) in Buddhism? These are the four sublime virtues.

Empathetic joy or altruistic joy (mudita) is the virtue of delighting in others' experience of well being and good fortune. Here, we may encounter people who are doing better than us, and we feel genuinely happy for them. This is the opposite of feeling jealousy and envy.

Compassion (karuna) is the virtue we feel when encountering the suffering of others, and wishing them, or even helping them, to alleviate their suffering. Here, we encounter people who are doing worse than us, and we feel like lifting them up. This is the opposite of feeling contempt.

Loving kindness (metta) is the virtue of wishing that everyone, without exception, be happy, healthy, at ease, content, and enjoy peace and well being. Here, we encounter all people, and we feel like being their ally and benevolent friend, who wishes them no harm and only wish the state of well being for them, just as we experience the state of well being ourselves. Of course, we also want to be our own ally and our own benevolent friend, who wishes well being for ourselves too. This is the opposite of feeling ill will and hatred.

Equanimity (upekkha) is the virtue of being even-minded, with unshakeable inner peace and freedom, in the face of fortune and misfortune, honour and dishonour, gain and loss, praise and blame, pleasure and pain, good health and disease etc. Here, as you have said, is the virtue where we accept all that happens to us with an even mind, and let go of the struggle against circumstances that are out of our control. Of course, we should still be mindful to improve ourselves the next time we encounter choices in life, that is in our hands - equanimity is not fatalism. This is the opposite of greed and discontent.

The four brahmaviharas, therefore, is the teaching in Buddhism that shows us how to relate to others and how to relate to ourselves, in all possible scenarios where: others are better off than us, others are worse off than us, we are better off than how we think we should be, we are worse off than how we think we should be, as well as the case, where others and ourselves are doing just fine and being happy, contented and at ease.

So, while you were struggling with balancing contentment and teaching empathy/ sympathy and feeling grateful, it turns out that these are not contradictions in Buddhism. In fact, you have not one, but four brahmaviharas that you can share with your kid.

When you are hungry, you eat. When you are thirsty, you drink. When you are tired, you rest and sleep. But you don't eat, drink and sleep all at the same time. Similarly, the four brahmaviharas do not contradict each other. They are to be used at different times, for different situations. But, the point is, you need them all.

Let your mind reside in these four abodes of brahma and radiate the expansive goodness that emanates from them.

In my understanding, Buddhism teaches that we should be thankful for exactly the things we have (not to desire more/less) but to trust in the unfolding of our life.

In passing, I'm not entirely sure that's an accurate summary -- but perhaps that's a separate topic.

I was lucky enough to be born into a productive family and am living a mostly positive life, etc.

mudita.

As mentioned in another answer, it's worth identifying the brahma-viharas

These four attitudes are said to be excellent or sublime because they are the right or ideal way of conduct towards living beings (sattesu samma patipatti).

I guess what im asking is what place does sympathy/empathy or even being grateful have in Buddhism

I think they're instrumental in not hurting yourself -- the converse, e.g. "craving for things you can't have, or craving to keep things you can't keep", is a cause of suffering.

They're also instrumental in not hurting others.

I can see how that narrative would work for me because i have the things i want, but for people who aren't as fortunate, how do you reconcile that in theory?

What if someone in your family, a friend, a child, a spouse, were homeless or a drug addict?

Maybe you'd want to try to help, to act on that (and in practice to do that you might need to change yourself in some way).

Buddhism teaches we shouldn't want more than what has been given to us

Buddhism also teaches "generosity" and "giving" as virtues.

It also teaches healthy and appropriate social relationships -- towards friends and family, employers and employees and teachers.

And it isn't only a matter of passive acceptance -- states like viriya (energy, strength, effort) are identified as instrumental or virtuous -- conversely there are kilesas

... mental states that cloud the mind and manifest in unwholesome actions ... include states of mind such as anxiety, fear, anger, jealousy, desire, depression, etc. Contemporary translators use a variety of English words to translate the term ... such as: afflictions, defilements, destructive emotions, disturbing emotions, negative emotions, mind poisons, neurosis etc.

How to teach sympathy/empathy in Buddhism?

Right, well -- for a five-year old ...

I don't want to say it's difficult or impossible to teach, but it might be an ongoing process (not a learn-it-once-and-you're-done kind of lesson, like learning to tie your shoes or whatever). For example I also associate it with bodhicitta; and the principle or final (i.e. the last remaining) motive of the Buddha, his motive for teaching.

One aspect of it, that maybe everyone should know, is "harmlessness" -- sometimes called the silver rule in English, or the "negative" formulation of the Golden Rule

The maxim may appear as a positive or negative injunction governing conduct:

1. Treat others as you would like others to treat you (positive or directive form)
2. Do not treat others in ways that you would not like to be treated (negative or prohibitive form)
3. What you wish upon others, you wish upon yourself (empathetic or responsive form)

Some of the Buddhist texts explicitly use this negative formulation -- for example from the Dhammapada:

129. All are afraid of the stick,
     all fear death.
     Putting oneself in another's place,
     one should not beat or kill others.

Another aspect is, beware of looking down on people, of seeing others as inferior.

In Buddhist doctrine, "compassion" is explicitly not the same as "pity" -- see What is the difference between 'compassion' and 'pity'?

See also The Buddha's Teaching on Unselfish Joy:

Mudita will also vitalize and ennoble charitable and social work. While compassion (karuna) is, or should be, the inspiration for it, unselfish joy should be its boon companion. Mudita will prevent compassionate action from being marred by a condescending and patronizing attitude which often repels or hurts the recipient. Also, when active compassion and unselfish joy go together, it will be less likely that works of service turn into dead routine performed indifferently. Indifference, listlessness, boredom (all nuances of the Pali term arati) are said to be the 'distant enemies' of mudita. They can be vanquished by an alliance of compassion and unselfish joy.

In him who gives and helps, the joy he finds in such action will enhance the blessings imparted by these wholesome deeds: unselfishness will become more and more natural to him, and such ethical unselfishness will help him towards a better appreciation and the final realization of the Buddha's central doctrine of No-self (anatta). He will also find it confirmed that he who is joyful in his heart will gain easier the serenity of a concentrated mind. These are, indeed, great blessings which the cultivation of joy with others' happiness can bestow!

The habit of comparing people and finding them different is identified as a cause of conflict:

Māna is a Buddhist term that may be translated as "pride", "arrogance", or "conceit". It is defined as an inflated mind that makes whatever is suitable, such as wealth or learning, to be the foundation of pride. It creates the basis for disrespecting others and for the occurrence of suffering.

See also How are 'conceit' and 'identity-view' not the same?

How does a child learn anything?

I don't know of any detailed Buddhist doctrine on that subject (the doctrine I have comes from studying Early childhood education in Ontario and Montessori education).

I expect that it will be by "modelling" (i.e. exemplifying, providing or being an example of) the behaviours you might want them to learn.

The Buddha does NOT say "just sit still and accept life for what it is". The Buddha says we should practice to benefit one and all (e.g., "to be grateful, empathetic, help others"):

AN4.95:3.3: But the person who practices to benefit both themselves and others is the foremost, best, chief, highest, and finest of the four.

Practicing to benefit one and all requires a shared understanding of one and all. Empathy is a start:

DN34:1.7.87: They understand the minds of other beings and individuals, having comprehended them with their own mind.

In that shared understanding is a form of acceptance. In that understanding is a simple acknowledgement of present perception. But we have to be very careful here. That shared understanding is perilously close to identification. Buddhist acceptance is NOT identification. So there is a problem with using the term "acceptance".

There is a problem with using "acceptance" to understand Buddhism. Buddhists will see anger but not accept it. Buddhists will see covetousness but not accept it. Buddhists will see ill will but not accept it. Buddhists will see lying but not accept it. Buddhists will see delusion but not accept it.

There is also a problem with using "not desire more/less" to understand Buddhism. It is a problem because the Buddha decided to teach the lessening and ending of suffering. The Buddha did not accept the apparent inescapable inevitability of suffering. And he shared the escape from suffering with a foundation of more love, compassion, rejoicing and equanimity.

In brief, teach sympathy/empathy without identification. It feels bad to be lied to, so don't tell lies. It feels bad to have things stolen, so don't steal. It feels bad when others are stingy, so be generous. Those are all examples of a shared understanding without identification.

Speaking as buddhist and a father of four (3 biological kids and 1 step-son).

I don't think we should teach the passive unfolding. Like, we obviously can't say: "if they provoke you and you get angry, you may have an impulse to hit them, just watch it unfold" - absurd.

Instead, we can teach them karma and how we always reap what we (or our previous generations) sow.

I.e. your family is not just lucky. You inherited the results of someone's hard work, good ethics, and kindness. Not necessarily your direct ancestors but in general some people who contributed to good circumstances that shaped your life. That said, we can't just rest on the old laurels, we must make sure in our own life we can preserve the good karma we inherited and pass it on to the future "us".

Those other kids are not just unlucky. They inherited results of someone in the past being stupid and/or lazy and/or wicked.

So we (the parents and kids) can empathize their condition, because it's hard to build good life on a bad foundation. And we (the parents and kids) should pray that they will intuitively discover what kind of behavior leads to a less troubled future, or may they encounter good role models who would show them how to create better future instead of perpetuating old problems.

In short, to me it's not about being greedy for more vs passively watching things unfold. I think it's about creating causes of trouble vs creating causes of harmony - and how this process spans past, present and future generations. Thinking in terms of karma we can be grateful, we can empathize, and we can aspire to do as well or better as our karmic benefactors.

P.S.

It's totally okay to desire less trouble and more harmony. In fact that's what Buddhist path is all about. Harmony is not just external comfort, you know, that's the coarse aspect of harmony. The deeper types of harmony are e.g. the social harmony, ecological harmony, and finally the inner harmony.

thankful for exactly the things we have ... shouldn't want more than what has been given to us.

This is not entirely accurate. We should accept what we have rather than wishing it were otherwise. Indeed, things are the way they are for a reason, and wishing they were otherwise is plain stupid not to mention unnerving. We have what we have and that's what we work with. We shouldn't want more shiny objects, power, and fame - because eventually they lead to trouble. Wanting more harmony for ourselves and for others is totally fine.