When people love each other, they tend to develop a feeling of care and compassion for the other person. Because we love them, we want them to be happy and in good health always. But sometimes it may happen that they don't want us to care for them, they might think of our care as our stubbornness or pushiness towards them which may impact the beauty of the relationship.
All of us are independent (that's what we think so) and are smart enough to make our own decisions. When someones tell us what to do and what not to do, we don't really see that as care; in fact, we see it as a kind of push to do something which becomes a burden or overhead for us.
Care is a feeling which is extremely loving from the givers' side but is not taken in the same sense by the receiver. There's is a reason behind that. There's a line between care and extra care (which we also call overprotective). Care is good and must whereas extra care is a big turn-off.
But when does care turn into protectiveness?
In any relationship, one person mostly becomes protective if the other person is too rash or careless. They tend to avoid or ignore the nitigrities which might be of great importance and hence comes the protectiveness. It arises due to a lack of trust in the other person to be able to do certain things as expected.
So I would not call protectiveness a push, it's rather a pull from the receiver because of their carelessness. The other person has to interfere more and care extra to cover up for the carelessness which looks annoying to the receiver.
Can a relationship survive without care?
Nope! It's a straight No. Care is an implicit feeling that comes automatically in a love relationship. If you love someone, you are bound to care for them.
So what is the solution to this problem?
The day you stop caring, the person would have a problem and your protectiveness is already posing a problem. So what to do? The care gives can't do much here. The solution lies in the court of the receiver, they must start getting careful about things and about themselves. If they are taking enough care of themselves, the other person won't have to, simple!