How do Miss Havisham and Orlick both want revenge in Great Expectations?

Miss Havisham uses Pip to get revenge on men, and Orlick wants revenge on Pip.

Miss Havisham is a troubled woman.  She was jilted at the altar by her fiancé, and ever since she has been in a deep depression accompanied by mental instability.  She uses Estella as her instrument of revenge.

Not able to get revenge against the man who jilted her, Compeyson, Miss Havisham adopts a daughter and trains her to be a tease.  She uses Pip, who is just a young boy from the village, to “train” Estella to be this instrument of revenge against the male sex.  Estella abuses Pip and makes him fall in love with her.

It is not until Pip is older and gets more information from Herbert Pocket that he learns that Miss Havisham has been using him.

"I don't say no to that, but I meant Estella. That girl's hard and haughty and capricious to the last degree, and has been brought up by Miss Havisham to wreak revenge on all the male sex."

…"Why should she wreak revenge on all the male sex? What revenge?" (Ch. 22) 

Pip didn’t know Miss Havisham’s history, or Estella’s, before this.  He didn’t realize how he was being used.  He still loves Estella, but he is irritated at Miss Havisham for having ruined his life.  Miss Havisham tries to explain or excuse her actions.

"Hear me, Pip! I adopted her, to be loved. I bred her and educated her, to be loved. I developed her into what she is, that she might be loved. Love her!"

She said the word often enough, and there could be no doubt that she meant to say it; but if the often repeated word had been hate instead of love—despair—revenge—dire death—it could not have sounded from her lips more like a curse. (Ch. 29) 

Miss Havisham did not target Pip directly.  He was a toy, and a target of opportunity.   He didn’t mean anything to her.  She affected his life, and changed irreparably the person he would become, but she did it for her own reasons.  She didn’t own up to it. 

Orlick directly targeted Pip, however.  He lured him to the marsh and kidnapped him. Orlick blamed Pip for getting him fired from Joe’s blacksmith shop and also for getting him fired from Miss Havisham’s later.  He also says that he turned Biddy against him. 

"You was always in Old Orlick's way since ever you was a child. You goes out of his way this present night. He'll have no more on you. You're dead." (Ch. 53) 

Pip is shaken by Orlick’s attack, especially since he says he will kill him.  It shows that Orlick is every bit as bad and unstable as Pip thought he was.  His revenge against Pip was personal, because he felt that Pip had targeted him.  Orlick admits he killed Mrs. Joe, so murder is not below him.