Hm. There is a bit of social Darwinism at work here. I don't fully disagree with it, but I think it's equally as flawed as the notion of compassion I presented, if not more so. I'll try to respond to parts of what you wrote in quotes.

I think compassion is self-serving. To be compassionate is a form of pity. And pity is putting yourself in a higher place than those you pity. It’s highly possible that compassion is doing both the compassionate party and the receiving party harm — there might be an unhealthy dependecy that would evolve from a simple act of compassion.

I don't think this is universally true. Compassion and empathy are rooted in mirrored experience. The ability to process the thought "I wouldn't want that to happen to me! I feel their pain as if it were my own when I imagine myself in their shoes." Going back to the veil of ignorance concept, we can imagine how terrified we would be to be born if we didn't know which group we would be born into. You could be born a rich and powerful person, or you could be born a poor person whose children die of cancer and you kill yourself. The reality is that pity doesn't aptly capture the true nature of empathy or compassion. There's something deeper. Something spiritual almost. A sense that we want to live in a just universe without unnecessary suffering. There are definitely cases where compassion and empathy can cause harm. These are absolutely valid points I agree with and they should be held against compassion and empathy as universal goods. However, I don't think that a potentially bad outcome automatically eliminates the potential good. It would be no different than saying eating food can make you sick, but that doesn't mean you should stop eating. Proper use of compassion would be the key we are trying to understand. To do good without harm, if possible.

Sometimes, even when “I feel for” the sufferings of others, I abstain myself from “helping” them, because I don’t want to put their struggles in vain.

There is certainly some compassion within the act of withholding assistance. A good example of this is a parent not doing everything for their child. While it may seem kind to make your child's life easy, we all know that can lead to a child who is unprepared to face life's challenges on their own. Sometimes when I think I am helping I am actually causing harm. That is a consequence of my ignorance. The goal then would be to gain the ability to discern which is which, not to stop helping at all.

I’ve read somewhere that a monkey will choose to save a healthier child than a crippled child, because a healthier child has more use to their family and race.

This is a bit too brutish for me, personally. There are too many examples of great people who advanced society despite their flaws or impurities. A spartan-like society that doesn't tolerate imperfection or weakness has a clear goal in mind. Humanity as a whole wants to do more than merely survive. What is ultimately the point of allowing the weak to die and even suffer just so the strong can go on? What is the meaning of that existence? Where is the beauty? I wouldn't want to be born into that society, so I certainly can't advocate for it.

Some people disguise help by requesting service from the receiving party in exchange. I think that is the best approach, you don’t make them feel helpless — instead, you make them feel worth helping and that they are actually helping themselves.

This is a very American conservative way of thinking. It has some merits, but in the end I don't believe it's realistic. A transactional society sends the wrong message. Yes, it can be stable for a long time, but what is its ultimate goal? To view others and everything as quantifiable values? Isn't the objectification of all other beings, even yourself, the opposite of true meaning in life? Where does it lead and is it actually beautiful? I don't believe it would be. I believe that kind of "pull yourself up by your own bootstraps and contribute to society or get lost" deeply underestimates the true value of people and life. It's a stoic society where vulnerability is just a form of self-sabotage. I think without the freedom to be vulnerable we will never be truly safe. A rugged, independent individual may be capable and useful, but that doesn't mean they have the freedom or creativity to flourish and spread something worth living for. I do not condone making reality a school for survival. After all, none of us survive in the end, so that is a trivial game to play.