Individualism is a tradition about valuing individual people. It says people are more than a social group, an ethnicity, a nationality, a religion, an educational level, a profession, an income, a marital status, and other broad demographic data. People have unique ideas, traits and preferences. As you can't judge a book by its cover, you can't judge a person without getting to know him.
Individualism says people should put themselves first. That doesn't mean to hurt others in any way. It just means everyone is responsible for their own life and own success, and should make that a high priority. Help others after you have your own house in order and have something to spare. This approach means no one is reliant on anyone else. It means if my life doesn't work out, that's my own responsibility. No one else is to blame and I am not a victim. This approach of personal responsibility is empowering because it means I can take initiative without waiting for someone else to help me.
Individual responsibility and individual success have another valuable aspect. It means people who make good decisions come out ahead, and people who make bad decisions don't. If everyone pooled all their effort, thought, resources and so on, then everyone would come out equally well no matter how good or bad their lifestyle. When good ideas result in success, that is useful feedback. It helps people know they're on the right track. It helps them know what to do more of. As a result, good ideas are repeated and spread. And on the other hand, when bad ideas fail then people learn not to do those bad ideas. They get useful feedback and can learn from their mistakes. Individual responsibility helps knowledge be created about which ways of life do and don't work well, and it helps errors be corrected.
None of this is to say other people aren't important or should be ignored. Cooperating with other people is wonderful. The best way to cooperate is for mutual benefit. If you cooperate so you both come out ahead, that's great. Who could complain about that?
Put another way, cooperation should be voluntary. If I consider some instance of cooperation the best thing to do, I will do it voluntarily. If I'd rather do something else, then I won't want to do it, and I would only do it if forced. Voluntary cooperation is purely good because everyone believes it is in their own interest and will have a positive result. Doing something with other people involuntarily, on the other hand, covers all situations where someone believes the result will be bad in some way and doesn't want to do it. The individualism tradition says it's best if all interactions between people are voluntary.
Voluntary actions are actions I'm responsible for. I chose the action and the consequences are mine, for good or ill. I take on the risk (possibly a small risk) of choosing to do something that may or may not work out, and I get the rewards of my choice. Under this system, if I often fail then I'll try to do better and learn something. Responsibility leads to improvement. On the other hand, if I do something involuntarily, and it turns out badly, I'm just going to say "I told you so" and have nothing to learn from it since I saw the result coming in advance. And whoever forced me (for example, the Government) has little incentive to learn or improve anything because I was the one who had to take actions that didn't work out, I was the one who was harmed, not them. They might not even know that it was a failure. It would take significant effort to monitor, and monitoring people is difficult and inaccurate. I know more about my life, and what works and what doesn't work, than any monitor. I could perhaps tell them what worked, but they might think I was just exaggerating, or was bitter, or they might not understand all the details of what I'm saying, especially if it's complicated. That's why voluntary actions are the best approach for error correction, and therefore the most rational approach.
Some people prefer to help others. They judge their own life as a success if they have helped others substantially, and not otherwise. What about them? Individualism doesn't object to that, as long as it's really what the person wants and he isn't being pressured or forced into it. However, individualism will generally advise against that mindset. If I help other people at my own expense, I limit my ability to be effective and helpful. To be most effective at accomplishing my goals, I'll need some reasonable level of prosperity, like food to eat, and health insurance (without which there is a substantial risk that I won't be much help to anyone). That's why individualism advises I put myself first (at least until I have enough for myself). After that, do whatever you want. If helping others is what you want, so be it, then you are voluntarily doing what you prefer, you are responsible for it, and you have every opportunity to learn from your results, improve and correct any mistakes you may be making.