Why did Deidara want to kill Orochimaru? In the anime it was shown that Deidara was so fixated on killing Orochimaru by himself, he also recklessly attacked Sasuke for killing(!) Orochimaru...


  It was shown that Deidara joined Akatsuki only after Orochimaru left,
  So what could be the reason for his desire to kill Orochimaru by himself?
  Is it said anywhere in story?
More information about Deidara can be found on this link:


  When Deidara's exploits caught the attention of the Akatsuki, Itachi
  Uchiha, Kisame Hoshigaki, and Sasori were sent to recruit him. Deidara
  refused at first but accepts a challenge from Itachi on the condition
  that the Akatsuki let him be if he won. However, Deidara was easily
  defeated by Itachi's Sharingan and begrudgingly joined the
  organisation. -> Chapter 359.
  
  His ego crushed since then because he admitted to himself that the
  Sharingan was a work of art, Deidara carried a murderous loathing for
  Itachi and the Sharingan for the rest of his life. Acknowledging that
  Itachi was a more powerful opponent, Deidara took steps during his
  time with the Akatsuki to get revenge on Itachi, such as training his
  left eye to counter genjutsu, and devising the means to create C4.


Now since Itachi easily defeated Orochimaru, Deidara wanted to defeat
him as well to show off and prove to Itachi that he is strong. You can
say, Itachi defeated Orochimaru, then he MUST defeat him as well.