A person under these circumstances has two choices. He can waive extradition and agree to be taken to the state that issued the warrant, or he can contest extradition, stay where he is and try to fight extradition.
However, there are only three grounds upon which you can successfully challenge extradition, and if those three don't apply, all he'd be doing by fighting the inevitable would be spending more time in jail where he is, for which he may not get credit when he's finally brought to the other state. The three grounds are:
1) he is the wrong person -- that is -- the warrant describes someone other than him;
2) he's the right person, but he wasn't in the state at the time of the alleged incident; or
3) the paperwork submitted by the wanting state's governor's office lacks the appropriate signatures. (The judge will look to determine that the paperwork is in order).
If the above don't apply, contesting extradition will be time-consuming and futile and it would be best for him to waive extradition and fight the case in the state that issued the warrant.
Typically, the holding state will assign a fugitive defendant a public defender to safeguard his rights, and he ought to confer with him or her as to what his chances are if he wants to stay where he and challenge extradition.
Bot***** *****ne -- while he can challenge extradition, it's typically pointless and he'll spend an extra month or two in jail right where he is awaiting a hearing that he will not win. Then he'll wind up being extradited after all.