Imagine you were aiming to appear to care about something or somebody else. One way you could do it is to work out exactly what would help them and do that. What could possibly look like you care about them more? The first problem here is that onlookers might not know what is really helpful, especially if you had to do any work to figure it out. So they won’t recognize your actions as being it. You would do better to do something that most people believe would be helpful than something that you know would.
Another problem arises if everyone knows the thing is helpful to others, but they also know that you could do the same thing to help yourself. From their perspective, you are probably helping yourself. Here you can solve both problems at once by just doing something that credibly doesn’t help you. People will assume there is some purpose, and if it’s not self serving it’s probably for someone else. You can demonstrate care better with actions which are obviously useless to you and plausibly useful to someone else than actions plausibly useful to you and obviously useful to someone else. Fasting to raise awareness for the hungry looks more sincere than eating to raise money for the hungry.
I wonder if this plays a part in choice of political leaning, explaining why economic left wing supporters are taken to be more caring. Left or right wing economic policies could both be argued to help society. However right wing economic policies are also supported by people who want to maintain control of their possessions, while left wing economic policies should not be except by the long term welfare dependent. This means that if you care about expressing care, you should join the left whether right wing policy looks better or worse for everyone overall. Otherwise you will be mistaken for selfish. If this is true then the best way to support right wing policy could be to popularise reasons for selfish people to support left wing policy.
Added 9/2/11: Robin Hanson gives more examples of people giving less usefully to show care.