Yeah, very common stereotype. Whenever you care for someone's well being more than they do for themselves, people see this as an example of not being capable of asserting yourself or allowing others to take advantage of you.
Even if its what you want, your choice, the receiving party has no power to force you to do squat and you can cave someone's face in if they tell you otherwise.
I gain far more pleasure making someone else happy than I do sitting in a box just tending to myself. I like to keep busy or at least always have enough to do in a day, and caring for someone gives me both those things. I am just me, taking care of me is something I do everyday anyways, but caring for someone else and making them happy is an amazing feeling, especially if they would be living badly without you.
I know of many schools of philosophy that say the path to true happiness is in living for the sake of others, not just yourself, but not exclusive of yourself either. Humans are a social species and in caring, both sides --not just the receiver -- are gaining the benefits.
The real thing people should think about is if you are
incapable of caring for others, thats a real failing. Not emotionally, but actually being able to be helpful.
Also on a scientific note: The protein coating on our chromosomes depletes with each division, and when its deteriorated enough no more divisions can happen and the cell can't divide any longer, thus giving it a sort of expiry date. However, a protein called telomerase is released when being cared for by others that restores this coating, thus increasing a cells lifespan and potentially a personal overall lifespan. Conversely, stress deteriorates this coating, suggesting that the difference of having someone caring for you or not can be seen physically and impacts lifespan and health.