If an iPhone 3GS can run iOS6, I am perplexed why the same can't be true for the iPad 1.
iOS 5 also doesn't run all that great on the iPad, so I'm sure that played into the decision not to offer iOS 6 as well. The 256MB of RAM paired with the large screen seems to be the biggest cause for this. The 3GS' hardware isn't great, but it's only powering a 320*480 display
(I know the 3GS also has 256MB of RAM but it's display resolution is much lower).
CPU, RAM, etc. are basically the same, but the iPad has to drive about five times as many pixels. Thus it effectively has much less RAM, an underpowered CPU/GPU, etc.
It's an odd and unintuitive situation, but despite being newer than the 3GS, the original iPad is ultimately a less powerful device, when it comes to which apps and OS releases it can support.
I'm sure Apple could support iOS 6 if they wanted to, but I imagine they decided that it wasn't worth the tradeoffs (e.g. poor performance, RAM available to apps, resulting stability or lack thereof).