Why is slavery ignored in the Constitution?
I believe that in the Constitution, there is not a single "slave" or "slavery", it just refers to them as "others." Like the provision where Congress was forbidden to prohibit importation of slaves, it said, "importation of persons." Were they focusing at a more general level or was this an attempt to ease the tension with the states that were pro-slavery and gain their support?
In 1789, Ben Franklin referred to the "peculiar institution" as it was sometimes called as "an atrocious debasement of human nature. . . ." However, the beginnings of the abolitionist movement would not really take root until the 1830's as a catalyst for increasing animosity and hostility between slaveowning states (by then, just the Southern and border states and the Northern states.
The failure of the Articles of Confederation had created what many considered to be a grave situation, wondering if the country that had lost so much in its fight for independence could actually survive as a nation, and the need for a central government was great. Therefore, although the issue reared its ugly head from time to time during the convention, it was usually glossed over without too much protest, especially as the document came closer to being finished, because no one expected it to be ratified if great compromises weren't made.
The Convention had representatives from every corner of the United States, including, of course, the South, where slavery was most pronounced. Slavery, in fact, was the backbone of the primary industry of the South, and it was accepted as a given that agriculture in the South without slave labor was not possible. . . .The cultivation of rice, cotton, and tobacco required slaves to work the fields from dawn to dusk. If the nation did not guarantee the continuation of slavery to the South, it was questioned whether they would form their own nation.
In America's Constitution, Akhil Reed Amar writes of the Constitution and slavery, "Slavery was the original sin in the New World garden, and the Constitution did more to feed the serpent than to crush it." By the mid-1800's the compromises and willingness to ignore something that needed to be addressed as the issue that reared its head at the Constitutional Convention became the focus of a nation at war with itself leading to the Civil War.
Actually, slavery was a very big issue at the Constitutional convention. Although the abolitionist movement had not begun, there were those who thought the practice should be ended first by stopping the salt water slave trade, followed by gradual compensated emancipation. Southern delegates threatened to walk out of the convention if slavery were not protected; while northern delegates adamantly refused. The deliberate omission of the "s" word was part of the several compromises entered into so that the Constitution could be completed and ratified. There was no question in anyone's mind about the true nature of the "elephant in the room," and there was no failure of resolve on the part of the delegates. Rather they had no choice but to use this seemingly inept euphemism if they were to write a constitution. They considered this the lesser of the two evils with which they were confronted. Robert Ellis in Founding Brothers has an excellent discussion on this point.
The word "slavery" is not used in the Constitution mainly so that the Framers would not have to admit what they were talking about. Southerners tended to like the term "servants" when they talked about slaves and many Northerners would not have wanted to dwell on the fact that they were condoning slavery. Today, we do not "kill" bin Laden but rather we "bring him to justice." Then, they did not have "slaves" but rather had "others."
We can tell that they are not trying to be, as you say, "more general" from the words of the Three-Fifths Compromise. There, they specifically excluded Indians, thus making it clear that the "others" could only be slaves.