To sin means to miss the mark. Sin has come to mean a lot of things in our minds but Jacob seems to be pointing out its most accurate and intended meaning when he specifically says the Jews “looked beyond the mark.” This tells us that God originally gives us what is good, and when we want more, or something else, he, as a good and patient teacher, assists us in looking beyond the mark (or in sinning).
“Looking” has more to do with “perspective” than it does a set of deeds. If the perspective is missed, then we have “missed the mark.” The Jews looked for a set of rules to govern their conduct. A set of rules was not what God originally intended for them. They missed the perspective, they looked in a different direction and got what they wanted.
When Alma says that Melchizedek priests “could not look upon sin save it were with abhorrence,” I’m not sure we can say that these priests never did things that were against a set of established rules, rather, after obtaining the perspective God gave to them, they abhorred altering that perspective, or going back to their old way of seeing things. They no longer “looked beyond the mark”. They were perfect in Christ and understood what that meant. Like Paul “all things were lawful” to them, but not all things were expedient. They were able to “obtain a sufficient hope by which [they could] enter into the rest of the Lord, from this time (right now) henceforth until [they] shall rest with him in heaven.” (Moroni 7)
“But behold, the Jews were a stiffnecked people; and they despised the words of plainness, and killed the prophets, and sought for things that they could not understand. Wherefore, because of their blindness, which blindness came by looking beyond the mark, they must needs fall; for God hath taken away his plainness from them, and delivered unto them many things which they cannot understand, because they desired it. And because they desired it God hath done it, that they may stumble.”
Wikipedia, Etymology of “Sin”
“The English Biblical terms translated as ‘sin’ or ‘syn’ from the Biblical Greek and Jewish terms sometimes originate from words in the latter languages denoting the act or state of missing the mark; the original sense of New Testament Greek ἁμαρτία hamartia ‘sin’, is failure, being in error, missing the mark, especially in spear throwing; Hebrew hata ‘sin’ originates in archery and literally refers to missing the ‘gold’ at the centre of a target, but hitting the target, i.e. error. "To sin" has been defined from a Greek concordance as ‘to miss the mark’".