Why are direct proofs often considered better than indirect proofs? As the title indicates, I'm curious why direct proofs are often more preferable than indirect proofs. 
I can see the appeal of a direct proof, for it often provides more insight into why and how the relationship between the premises and conclusions works, but I would like to know what your thoughts are concerning this.
Thanks!
Edit: I understand that this question is quite subjective, but that is my intention. There are people who prefer direct proofs more than proof by contradiction, for example. My curiosity is concerning what makes a direct proof preferable to such individuals. In the past, I've had professors grimace whenever I did an indirect proof and showed me that a direct proof was possible, but I never thought to ask them why a direct proof should be done instead. What's the point? 

Even if direct proof is preferable, it's not always possible.  How could you prove, for example, that primes are infinitely many, except by showing that any finite number we assign to them entails the existence of yet another prime (Euclid Elements, IX, 20)--[edit] or contradicts something else known to be true, e.g. the divergence of the harmonic series (Euler)?
Proof of any kind of unlimited multitude, it seems, has got to be indirect, i.e. by contradiction. 
