Is the abandonment by a non-believer in 1 Cor. 7:15 an example of marriage covenant-breaking sin?
Among Christians who take scripture seriously, there are (usually) only two categories of action which might justify divorce (defined as "legally recognizing that the marriage covenant has been broken by some egregious sin"):
- Porneia ("fornication" -- Matt. 5:32, Matt. 19:9)
- Abandonment by a non-Christian spouse (1 Cor. 7:12-15)
Marriage dissolution is (as you might expect) a contentious issue: some Christians would like to include many things as justifying divorce, and some Christians want to tightly restrict these justifications (or even deny that the marriage covenant can be broken at all). This causes a lot of discussion about what constitutes porneia and what represents abandonment (for example: is committing a sin which gets you thrown in prison the same as abandonment?). These discussions are outside the scope of this essay.
Certain conservative commentators (e.g. Bahnsen, Otis) claim that porneia is a sin which includes the abandonment of 1 Cor. 7, rather than being confined to certain types of sexual sin (e.g. adultery, homosexual sin, bestiality). The advantage of this view, theologically, is that it allows us to take Jesus statement about porneia in Matt. 5:32 -- "except for fornication" -- as representing the whole category of sins which break the marriage covenant. This way, it harmonizes nicely with what Paul claims in 1 Cor. 7:12-15, where he (apparently) allows for a non-sexual breaking of the marriage covenant.
I will suggest an alternative understanding of 1 Cor. 7:12-15, in which the act of abandonment by a non-Christian spouse is neither classified as porneia, nor as a marriage covenant-breaking act. Rather, Paul seems to imply that the act of abandonment should be taken as a performative (and thus legal) claim (by the non-Christian spouse) about how that spouse understands (and understood at its formation) the "marriage" in question. This performative claim shows that the original union was not a Christian covenantal marriage, and therefore no marriage covenant was broken by the act of abandonment.
Marriage is a covenant
Consider the following case:
A girlfriend and a boyfriend move in together, initiate a sexual relationship, and even have children. They do not make any vows, register their marriage with any authority, or even represent themselves as "married" to anyone else.
Are they "married" in a Christian, covenantal sense?
Most Christians (I think) would answer "no." Of course, some Christians claim that the sex act is a de facto, performative covenant commitment, but there are scriptural problems with this view (e.g. Deut. 22:28-29, compared with Matt. 19:6).
Christian marriage is a covenant commitment to faithfulness by a man and a woman, through a public (i.e. before at least two witnesses) oath, with the expectation by both parties that this covenant commitment will be life-long -- thus unbreakable by man (Matt. 19:6) except through some egregious sin (porneia, Matt. 5:32).
When non-Christians enter into a "marriage-like" arrangement, they often do not have the above view. Even if a couple go through a "church wedding", they often are not committing themselves to the above definition. They might even see the marriage as either:
- a "contract", which can be dissolved by the mutual agreement of both parties
- a "socially-constructed relationship", which is ontologically dependent upon some persistent mental or emotional state (e.g. happiness) in both parties
The Christian view of marriage (as a covenant commitment for life) has not been the norm, historically. It certainly was not the norm in first century Corinth or even in the Roman empire as a whole. William Buckland (an expert on Roman law) writes:
marriage in the law of the Roman Empire had at first sight a look very different from that of modern English marriage. It was dissoluble not merely by consent but, at any moment, by either party ... 
Paul, as a Roman citizen, would not be ignorant of Roman marriage law. He would understand that a couple who were married in the Roman empire were not committing themselves by oath to a covenant (such covenants require mental understanding and consent). In this context, therefore, the abandonment of a Christian by a non-Christian can be interpreted as a performative declaration of their own understanding of the original "marriage-like" arrangement: that it was not a life-long commitment, and not a Christian marriage covenant.
Even if the Christian spouse considered the relationship (on her part) as such a covenant relationship (and Paul advocated this: 1 Cor. 7:12-13), this understanding would not legally bind the spouse. On this understanding, the act of abandonment by the non-Christian was not a covenant-breaking sin, because there was no Christian marriage covenant to break.
Therefore, Paul's "allowance" of marriage separation/divorce in 1 Cor. 7 was not an addition to (or implicit expansion of) Jesus' divorce exception (porneia) in Matt. 5:32. Paul was merely encouraging Christian spouses to commit themselves whole-heartedly to their previous "marriage-like" relationships (1 Cor. 7:12-13), but not to force their own (perhaps new, post-conversion) understanding of this relationship (that it was a life-long covenant, unbreakable except by egregious sin) upon an unwilling spouse (1 Cor. 7:15).