It wasn't hiding something nasty.
First, AT&T didn't divest and re-acquire. The AT&T that you know today isn't the AT&T that sold off AT&T Wireless. For a little telecom history...
AT&T (the long-distance company) owned AT&T Wireless and other ventures like AT&T Broadband (which was sold to Comcast). AT&T Wireless eventually got bought by Cingular which was a joint-venture of SBC and Bell South (two local telcos). AT&T (the long-distance company) was bought by SBC in 2005 because, well, long-distance was dying. Given the AT&T brand, SBC re-branded itself as AT&T. In 2006, SBC bought Bell South giving them 100% ownership of Cingular which they decided to re-brand as AT&T.
So, it's really that AT&T Wireless was bought by Cingular (SBC/Bell South) and SBC ended up buying AT&T (the long distance company) and Bell South and re-branding the whole thing as AT&T. But it's really AT&T->Cingular (SBC/BellSouth)->Cingular (SBC) and then SBC re-branded everything to AT&T.
--
As another point, "cellular was clearly a growth industry a telecoms company would want in on" isn't necessarily true at the time. Cellular had very high costs compared to things like long-distance service. I mean, I remember when 10 cents per minute was a low rate for domestic long-distance. AT&T owned AT&T Wireless and spun it off in 2001 as a separate company. Even before Cingular bought them in 2004, AT&T had decided that wireless wasn't for them.
Was it short-sighted? Definitely. SBC bought AT&T (the long-distance company) for $16B while Cingular bought AT&T Wireless for $41B. AT&T made a lot of bad decisions during this era. They also wrote off home broadband. They spent $105B creating AT&T Broadband and then sold it to Comcast for $44.5B.
However, even with its broadband divestment, it's unclear whether AT&T Broadband was ever worth $105B. I mean, Comcast is a $189B company today and it looks like it was a $58B company before buying AT&T Broadband so over the course of 18 years, AT&T Broadband hasn't justified a $105B price tag. AT&T just way overpaid for being in an industry. At $105B, even if it grew to $189B, that would be 3% returns (and AT&T Broadband by itself isn't worth AT&T Broadband + Comcast + NBCUniversal + etc.). Point being, while broadband seemed like a growth industry that any telecom should want to be in, it was also an embarrassing money pit for AT&T. AT&T Broadband would never have justified the $105B they spent creating it.
Part of this is how the value of industries go. Sprint merged with Nextel in a deal valued at $72B. Today, Sprint is worth a third of that. So, even with hindsight, it's unclear that wireless is such a growth industry. AT&T (the SBC version) has done well out of it, but the industry is littered with poor-performing companies.
For example, take T-Mobile. It's been doing well recently, but it hasn't been a good investment for Deutsche Telekom. They bought VoiceStream for $35B and Powertel for $24B and SunCom Wireless Holdings for $2.4B bringing a total of $61.4B. Today, 18 years later, T-Mobile US is worth $63B, but Deutsche Telekom only owns 66% of it. So, Deutsche Telekom has lost a lot of money in the US wireless industry, even more so if you factor in opportunity cost over the past 18 years.
Likewise, AT&T Wireless was bought for $41B and was a substantially weaker company than Sprint is today. T-Mobile is buying Sprint for $26B. That's a Sprint with way more spectrum, way more customers, and way more cell sites than AT&T Wireless had. Sprint today is a more valuable company than AT&T Wireless was, but in hindsight we see that wireless companies weren't worth nearly as much as we thought they were.
In certain ways, the industry is crap. AT&T and Verizon basically showed that you could make money if you became giant. However, the industry also shows that if you're an also-ran, your future isn't bright. AT&T Wireless, as a competitor in a larger field, probably wasn't such a growth business that you'd want to be in. Purchasers of wireless companies have usually had to invest a lot in new spectrum and new networks and it really only made sense if you achieved a certain amount of scale - AT&T or Verizon-like scale.
The fact is that most wireless companies have done really badly. No investor today would go back and buy T-Mobile when it was launched in 2001. They spent over $60B on something that they were willing to sell to AT&T for $39B a decade later.
AT&T (the long distance company) sealed its fate by ignoring the future technologies (broadband and wireless) that would dominate our lives. However, it's unclear if they would have succeeded if they had held onto AT&T Wireless. Most wireless companies have declined in value over time and the two that haven't might have escaped that by creating a virtual duopoly. I know it's easy to look at the wireless industry and think, "everyone in America is paying them lots of money." However, most don't seem to hit the scale necessary to be good businesses and most have been bought for way more than they were worth.
It's easy to think of wireless as a growth industry that anyone would want to be in on. However, the history of the industry shows that most of the time it's been a losing proposition. Cingular definitely over-paid for AT&T Wireless. Sprint and Nextel definitely weren't worth the $36B a piece that they merged at. VoiceStream and Powertel definitely weren't worth the $35B and $24B that Deutsche Telekom paid for them. So, yea, AT&T (the long distance company) got rid of its Wireless business, but most wireless businesses were money pits that went down in value.