I came across a quote today, it is,
As a person it's what's on the inside that counts. It's what's on the outside that matters.
Please explain the quote for me. Are count and matter opposites?
In fact in this case, count and matter are actually synonyms.
Both mean “is significant”.
However, I suspect that your quote is wrong, and it should be
That is, it's someone's heart and intentions which are important, not what they seem to be.
In this example count and matter are synonyms. This is just a way of saying that they both count/matter, and lets the reader make his pick according to his principles :)