Just because the character cares for others doesn't mean they like them.
Needs a Better Description
Some say that love and like are similar because the two words share a positive feeling towards another. However, in this trope, there's a difference. Like implies that you are interested in something. However, love is a strong emotion. It makes us strong, it makes us change our ways, it makes us crazy, and it even makes us evil. Another way of displaying this trope is in dysfunctional bondings. A pair Vitriolic Best Buds will care for one another, but that doesn't mean they will like each other.