Why do you think the speaker of the house is next in lineto become president in the event of the death of both president and vice president

I think that this is because of the high importance of the Speaker as the representative chosen by the people.

People choose the members of the Congress, which has two chambers. The leader of the other chamber, Senate, is already in the line of succession as the Vice-President.

The leader of the other House is the Speaker of the House of Representatives and this person was a good choice for the line of succession since they're elected by (and from) the people who were elected by the population of the country.