I'm reading through the books of Samuel currently, and it had always perplexed me why David kept Joab around--Joab being rather a "hothead" whose actions typically got David in trouble with his people. If you doubt this, witness how easily Absalom won their hearts to usurp, albeit temporarily, the kingdom. Then, perplexingly, David chooses Absalom's general, Amasa, as his general once Joab has defeated Amasa in open battle. What is going on?
A key to this may be understanding who Joab (and his brothers Abishai and Asahel) was, and who Amasa was. Joab was David's nephew, the son of his (presumably) older sister Zeruiah, and Amasa was David's brother-in-law, the husband of David's sister Abigail. Given that David had seven brothers and at least two sisters, we can presume that he was most likely about 20 years younger than his oldest sibling, and hence Joab may have been close to David in age. Amasa, on the other hand, was likely somewhat older.
Now how did the "sons of Zeruiah" come to David? The Bible does not say specifically, but it's my guess that three young, hot-headed nephews of David came to that camp of 600 men out of support for David, and he felt morally obligated to keep them even when their actions got him into trouble. Then, when Amasa stood up for Absalom, David had the only person he could choose to replace Joab; an older relative.
It's all speculation, of course, but it does seem likely that a lot of the achievement, and a lot of the trouble, of David's reign had to do with how his family stuck together.
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