That is fine but you have already put it relative to what you think. If everybody does that, then morality will differ from a person to another; and thus it becomes meaningless.
But the words aren't meaningless just because we might disagree on some edge or corner cases.
The thing is, lots of people use words all the time without getting analytical about it. My daughter is 5 and knows what right vs. wrong is, but I doubt she could explain it to anyone without it just being circular.
When people use the words "right" and "wrong" (and all the related words such as good and bad and moral and immoral), most of the time they all pretty much agree with what it is. Stealing is wrong, cheating is wrong, killing is wrong. Helping someone who is hurt is right.
You can come up with scenarios where there are ambiguities, sure, just like with up and down, but most people agree on the basic ones.
You just have to let go of religious distortions of the concept. Take a step back and look at it more from an evolutionary biology perspective.
To me it has to do with aligning your goals with the goals of others. It is a very important concept for a social animal, especially one with high degree of cognitive sophistication such as humans, to have.