A friend tells you he read somewhere that rotting garbage can turn into maggots, which are fly larvae, and the maggots then can grow into adult flies. What part of the cell theory could you use to refute his claim?

Maggots will not form out of organic waste on their own. Its a variable dependent on fly, laying eggs on the garbage.

A friend from US instructed me that this is Biology experiment on US High schools.

So basically you would disprove this by holding an experiment - put some organic waste into two jars. Close one jar with a lid immidiatedly. Eventually, the open jar will produce maggots, the closed one doesnt.

Maggots forming on the waste = dependant variable. Lid on the jar = independant variable. opened jar = group control.

Whether the maggots form on the waste or not is dependant on the existence of independant variable - the lid. If there is a lid, maggots wont form, if there is not, they will form eventually (but, by the cause of other adult flies)

Group control is in place to prove what would happen if the independant variable was not in place (because someone could claim that regardless of the lid or not, no maggots would form on the waste)

In your situation, fly laying eggs would be the independant variable. Whether the maggots form out of the garbage or not fully depends if a fly layed eggs or not. Its not disprovement via cell theory (for that refer to the first answer) but it makes sense.