Why do many Protestant congregations not require attendance at services on Christmas and Easter? It came to my attention from living, driving around and listening to Christian radio that many Protestants do not have any services on what Catholics would consider solemnities (Christmas and Easter in particular) and even the most lax Catholic will attend if only to appease their mother. 

One of the precepts of the Catholic Church is to attend Mass on Sundays and Holy Days of Obligation, another is to receive the Eucharist at least once a year, particularly during Lent. That's why Mass attendance ought to peak around Easter.  But it would seem that some non-catholic congregations in the United States have adopted an opposite position.  

If you asked any given pastor what the reasoning behind this is, what might they say?
As far as I'm aware there's no biblical basis for requiring the church to gather at those specific times. For example there's no mention of Jesus' birth being explicitly celebrated as an occasion in Acts as far as I'm aware.

The congregation I belong to used to meet in a school as we didn't have our own building. We felt it was important to give the school caretakers a break at these times, so our church didn't meet during the school holidays (although we were encouraged to visit other churches or arrange other activities).