These are my opinions based on my own experiences (and study).
Empathy is not a gift to be given to others. It is a domain (and a means) of sensation, perception, and knowing; similar to vision, hearing, and so on.
I think that what you refer to as ‘giving empathy’ would be more accurately described as ‘giving compassion, patience, kindness, etc.’
But empathy itself–like all other sense-capacities–is more of a gift for yourself. Imagine what it would be like to drive a car that had no windows/windshield. Just a solid metal box with no way to visually perceive the streets and landscape around you.
That is like walking through the world with no empathy.
Ultimately, empathy is describing the capacity to develop an accurate sense of what someone else is experiencing. What you do with that sense is another question entirely. Some people use their empathy to harm or manipulate others. Of course, those people are usually sick, developmentally stunted, or significantly dysfunctional some way. But I imagine it occurs commonly enough.
So in my terms anyway, I’d describe what you’re thinking about as compassion, grace, and generosity of spirit.
And then, I think the question of how to cultivate those qualities is actually kind of funny in this case.
Because the answer is: ‘By developing empathy’.

You are sitting at home with a pail of water next to you. Suddenly, you smell a faint whiff of smoke. Looking up you see that the cigarette that your friend just threw into the garbage was not properly stubbed. It has ignited the paper in the trashcan. There’s a little fire starting up. You say, ‘sheesh. that’s the last time I let him smoke in here.’ Then you pour the water on the fire, and go on to have a wonderful day.
But what if you have a cold? You can’t smell anything. It may take you a much longer time to detect what’s going on. If we’re very unlucky, the situation may have advanced to a small crisis before you are aware of it.
Compassion and understanding in this metaphor correspond to pouring the water onto the flame. Empathy corresponds to your sense of smell and your ability to use it effectively.
If you can smell the smoke and see the fire, then it’s natural for you to handle it effectively. That doesn’t even make you a ‘good’ person or a ‘better’ person. Just a reasonably competent person.
Many of the times that I’ve created interpersonal problems in my life, one of the significant factors was that I did not have an accurate sense of what others in the situation were experiencing and how they were thinking.
For most of us, if we can clearly sense another person’s pain and need, and if we can help with it in some way, we usually will. It’s not because we’re good people. It’s because the experience of sensing pain is painful. That’s why another common alternative is to take some action that decreases our sensation of the other’s pain or discomfort.
Anyway. This has become quite the lecture, hasn’t it?
A little bit more:
People, in an effort to appear more impressive and more competent, usually practice hiding our needs and our pains from others around us. Sometimes that is a very appropriate move. But it has the (often unintended) effect of making the underlying motivations for our choices somewhat mysterious to others. And people can’t handle mysteries. The average person hates saying, “I don’t know”. So instead we create our own guesses and theories about people’s motivations, and we just take those as being accurate and real. They’re often not.
If you can clearly imagine the hidden needs and pain that are motivating people’s behaviors, you’ll find that it’s gradually becoming easier to have compassion for them.
The other side of this is to very intentionally and persistently seek out the compassion that you need. Look for places and people that are available and willing to give you what you need. Go get a massage. Talk to a therapist. Masseuses and therapists are people who make themselves available to meet people’s needs for comfort, attention, and emotional support. There are lots of others too.
And you don’t just have to pay people, also look for those people in life who seem to be kind. Try to spend a little time around them. Getting your own needs met, will help you to be more patient and attentive to others.
We’re all working on this. I know I definitely am. You’re not alone.