For brevity, abbreviate as CP 'Conditional Proof', as DM 'Direct Method, and as IP 'Indirect Proof'.
Source: p 445, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley
Indirect proof provides a convenient way for proving the validity of an argument having a tautology for its conclusion. In fact, the only way in which the conclusion of many such arguments can be derived is through either conditional or indirect proof.
I comprehend that to prove an argument containing only Conditional Statements (as all its premises and conclusions), you must assume separately some antecedent, because otherwise, with what else can you start the proof?
In despite of my comprehension above, I am still troubled by the bolded sentence above:
Why do CP and IP succeed where DM fails? After all, any method is operating on the same premises and conclusions; so it seems strange that CP and IP can abstract something more from the same argument than DM can.