The children of Reuven and the children of Gad had much livestock…The children of Gad and the children of Reuven came and said to Moshe, “…the land that Hashem smote before the assembly of Israel, it is a land for livestock.”…They approached him and said, “Enclosures for the flock we shall build here for our livestock and cities for our children.”…Moshe said to them, “Build for yourselves cities for your children and enclosures for your flock…”
Be’er Yosef: A midrash, partially cited by Rashi, notes the inversion of the order when Moshe speaks of the cities and pens. The petitioners had given the enclosures pride of place. This evidenced that they apparently attached too much attention to their livestock, and not enough to their children. When Moshe paraphrased their offer, he placed the children front and center, with the animals bringing up the rear of the contract.
It is impossible to accept this at face value. It certainly cannot mean that they valued their property more than their children – something unthinkable of most people on the planet, let alone people who had stood at Sinai, and benefited thereafter from the tutelage of Moshe, Aharon, and Miriam.
Their error, most likely, was far more subtle. It is easy to see why they would speak first of tending to their cattle. It was a far more formidable task than settling their families. The latter had where to go. The Torah reports that Sichon rebuffed the requests of the Bnei Yisroel to pass through his land. Not only did he turn down their peaceful request, but he answered it by assembling all his people to wage war on them. Rashi comments that HKBH did them a favor in setting up Sichon for his intemperate response. Rather than burden them with a protracted military campaign, HKBH encouraged the Emorite nation to seek battle with the Bnei Yisrael. They gathered en masse, and were thoroughly trounced.
A consequence of this is that their cities remained intact; the battle was never taken to the populated areas. Bereft of defenders, the conquering Jewish army effortlessly took control of the cities. There was no shortage of free living space for the Bnei Gad and Bnei Reuven. Cattle enclosures were a different matter. As those two shevatim were particularly laden with animals, they would have to get busy building suitable quarters for the livestock. This would explain why they mentioned the animals before the people. The arduousness of the task left it foremost in their minds.
Moshe’s objection was not that they undervalued their families, but that they failed to understand proper Torah chinuch. Jewish life must revolve around Torah and mitzvos. It is incompatible with cities and buildings named after false gods, or celebrating their exploits. Moshe argued that the conquered areas were not move-in real estate. Neighborhoods, buildings honoring objects of idolatrous devotion would have to be razed or altered to the point that they no longer would be associated with their past. (This is included in the Torah’s intent in commanding, “You shall utterly destroy all the places where the nations that you shall possess worshipped their gods.”) Failure to do so would lead to harmful effects upon their children. New institutions would have to be built as well – school, shuls, and batei medrash – that would carry the Name of HKBH.
This fundamental shift in emphasis is reflected in the verbs they used. In setting forth their proposal to Moshe, the Bnei Gad and Reuven said that while they would join the rest of the nation in fighting the wars of conquest, “our small children will dwell in the fortified cities.” In other words, they could be settled quickly in the cities left behind by the Emorites. Moshe, on the other hand, was precise in his instructions. “Build for yourselves cities for your children,” he said, underscoring that they could not rely on the abandoned Emorite habitations.
Moshe’s words were not lost on them. “The Bnei Gad built Divon and Atarot…The Bnei Reuven built Cheshbon and Elaleih.” Some places, they built anew and assigned old names. “And Nevo and Baal-Meon [they rebuilt] with altered names…and they called them by other names instead of the names of the cities that they built.” Others, as Rashi explains, they took pains to invent new names, rather than the ones that had been used in the past, because they were connected to avodah zarah.
Why had they missed this point? Why did they have to be instructed by Moshe? We can safely conclude that their preoccupation with their cattle, with their material possessions, blinded them to the realities of proper chinuch for their children.
 Based on Be’er Yosef, Bamidbar 32
 Bamidbar 21:23
 Devarim 12:2
 Bamidbar 32:17
 Bamidbar 32:24
 Bamidbar 32:34-35
 Bamidbar 32:38