Verse 24 gives a concluding statement as to why Israel was taken into captivity. There are two possibilities regarding Israel's Sabbath breaking. 1) Israel completely rejected God's Sabbath for another day. This possibility exists due to the instances of the "My/their" or "Mine/yours" contrast, that is, My Sabbath as opposed to your Sabbath. 2) They polluted the Sabbath by careless, self-centered observance.
The probability is that they did both—some people completely rejected the Sabbath, while others carelessly observed it. However, it was because of Sabbath-breaking, a type of idolatry, that they went into captivity.
When we look at secular history, even biblical history, and society around us, how to keep this day is a mixed bag. On the surface, what we see in the New Testament is rigorous legalism from the Pharisees or asceticism from the Gentiles. Today, we might call that an extreme "rightism" or perhaps a reactionary conservatism.
In today's world, though, we are confronted with the other side of the coin. We do not even begin to know how to keep the Sabbath because, from our earliest days, our culture's emphasis has been on Sunday, a day that cannot be kept holy because it was never made holy!
The cycle of six workdays and one day of rest and worship is a legacy of the Bible. But in fairly recent history, society has undergone a radical transformation because of scientific, industrial, and technological achievements. A shorter workweek provides us more leisure time. Businesses, however, make every effort to make the best use of time, to maximize production by scheduling work shifts so that the weekly cycle becomes a blur.
We have come to the place where we think that time totally belongs to us, and we can use it as we good and well please. This, in turn, makes a person very conscious of his free time. What does almost every individual do? He does the same thing that a business does. Every bit of time in a person's life is booked up because he wants to get the most out of life.
Even among those who are reasonably religious, the result has been that Sunday has become the hour of worship. The older among us can probably remember that, in the community, Sunday was once set aside very seriously. People did not work. They usually spent the day at home. Maybe the most secular thing they allowed themselves to do was to read the Sunday newspaper. Some, perhaps, did not even listen to the radio on Sunday because, to them, the day was holy.
But over the years, Sunday worship—which used to be kept somewhat as God expects us to keep the Sabbath—has now become, even among religious folks, an hour rather than a day of worship. People go to church for that one hour then perhaps return home. Or, maybe they go to a Sunday brunch at a restaurant. They spend the rest of the time on that day either making money or seeking their own pleasure.
All the while, the real Sabbath is ridiculed or ignored. This is what confronts us when we begin trying to keep it. A similar environment even affects those who continue to keep it. When we look in the Bible, we find that God does not give us many specifics as to how to keep it. God does, however, give us a number of broad principles, and He expects us to extrapolate from those principles in applying them.