Some people don't want to get up [out of bed] simply because they don't like the activity that awaits them.
However, change the context and the article the to an and 'irritates' fits nicely:
The point being made by the test source (click here)
is that 'activity' does not refer back to 'don't like to get up':
Some people don't want to get up at the game and participate in the human wave simply because they don't like an activity that irritates them.
She became the first woman to have been elected mayor of Chicago.
To me, stative became and the infinitive passive perfect have been elected just don't sit well together unless a timeline is stated:Noteworthy pattern,
In the short period of five years with Gearhouse, Belinda Loockx became the first woman to have been appointed ...
In 1924 Epstein became ‘the first woman to have been honored ...
In January 2001, this Government became the first to have been elected under the new electoral provisions of the new Constitution.
She was the first woman to have been elected to both houses of Congress and in 1964 became the first woman to have been nominated for the presidency of the ...
Hope that helps some.