That fight was the first of many, and allegedly Apple CEO Steve Jobs began looking into a jump to Verizon at that point, very early into the relationship.
While the company looked into Verizon "seriously," the move would have required developers to build the smartphone "from scratch" all over again, moving from GSM to CDMA. There was also, of course, the exclusivity pact with AT&T.
Additionally, there were other battles, such as over tethering, where AT&T wanted to charge, and Apple wanted it included in the monthly data plan. The ability to tether now costs $20 extra per month.
There is a lot more to the story. Finish it here: Bad Connection: Inside the iPhone Network Meltdown