Why is causing pain to others bad? Why do you care about what other people feel?
Quid pro quo. I care about them and don't cause them pain; and in return, they care about me and don't cause me pain. It's also called the social contract.
You may argue, "prisoner's dilemma" style, that an individual can then gain an advantage by breaking the social contract, and indeed some people do that. Bruce Schneier wrote a whole book about that topic. But as it turns out, most people don't break the social contract, due to 1) intense social conditioning (religious or otherwise) and/or 2) the threat of punishment if they're caught.
The social contract predates Christianity by millenias; heck, it presumably existed in a primitive form in stone age hunter-gatherer culture.
But even ignoring social conditioning and even the evolutionary traits that have developed to promote that contract (e.g. increased empathy), abiding by the contract still makes sense: Civilization depends on the majority following the social contract, and indeed, most people find that the immediate benefit of breaking the contract is outweighed by the threat of civilization falling apart. Of course, once people start to break the social contract in larger numbers, the cost-benefit ratio changes, and civilization crumbles quickly.
Surely you've heard of the Golden Rule? This requires zero belief in the supernatural or any sort of sacredness.
Except that it doesn't explain why you should follow it. Most people seem to use "karma" (or "what comes around goes around") as a not-quite-as-supernatural-as-an-omnipotent-God reason for following the Golden Rule.
I'd argue that karma is a real thing, only global, not personal. When you do a good thing for others, you increase global karma, ever so slightly increasing the odds of good things happening to you, too. (But it's a big world; I think you'll find playing the lottery has better ROI.)
Personal karma AKA the "just world" belief is of course a myth. The fact that so many people believe in it is a testament to the aforementioned social conditioning.