hearsays & popular opinions:

"The earth is moving because that's what I learned in school - and what we learn in schools is automatically always true, even if unproven.

"Everyone who's hip and modern thinks the earth is moving. 'E pur si muove!'" (Notice how 'modern' Galileo Galilei sounded when he allegedly spake a dead language). 

organizational ruling argument:

Taking a band of American federal government employees (NASA) at their word as if they need not provide any evidence.

majority argument: 

There supposedly being a "consensus" on heliocentricity among current cosmologists (but so was there a consensus on pseudoscience such as alchemy - so was there a consensus on Phrenology, Telegony, Phlogiston... and so forth, i.e. all by itself this line of reasoning is fundamentally unscientific).

superficial analogy:

"The earth is like a moving train... or like an airplane or something, that 's why we don't feel it move" (completely ignoring the fact that we actually do feel it [however lightly that may be] when a train or a plane moves)

the "it's too complicated - only experts know it" argument:

Watcheing a motion picture of the earth move by means of special effect simulations on docu/info-tainment programs somehow means it must be moving? Nope!

personal convictions:

 "I believe it's moving because so many people today can not be fooled like that" (as if there is a natural maximum limit on the number of people who can fall for one deceit).