Intel at the time was shipping P4 Netburst CPUs. They had all the features, like multiple cores and 64-bit support, but also one huge disadvantage: they were power hungry, and it dissipated all that heat. Definitely not something you could put into laptops.
So the next generation, Core Solo/Duo, was not continuation of Netburst, but Pentium M, their mobile line which itself forked off P6 (Pentium Pro). They were released in January 2006, and were indeed 32-bit. The reason was time to market, they were basically throwing away their current arch and forking from an older branch; for the majority it was not a problem, most people were running 32-bit XP anyway, with PAE if you happened to have more than 3,5 GB of RAM (pre-SP2 XP supported that). Then, the 64-bit Core 2 Duo was released in July 2006.
The unfortunate part is, that Apple announced transition to Intel in mid-2005, and shipped the products across all lines in January-August 2006, i.e. hitting the window when only the 32-bit version was available. That means, that they had to define and maintain i386 ABI for their OS just because they ever shipped Core Solo or Duo machines. If they were able to ship C2D from the beginning, they could have skipped i386 and just use amd64 ABI from the start.
