I just have a cheap pair of wired headphones with an inline mic with a mute button. I'm using an old iPhone 5 since I just broke my Nexus 6 screen. In Android, this button was a very quick way to mute and un-mute calls, crucial during conference calls. I just tried this for the first time on the iPhone and it hung up the call instead. Is there anyway to change this behavior to mute instead?
No, there's no way to change this. I really don't like that Apple has decided the single-click on the headphone switch will disconnect the call instead of muting the microphone.
You can do what I have and go here to provide iPhone feedback to Apple to make this change.