How about the headset that came with the phone? This shouldn't need any jiggering to make it plug in properly.
I would also agree with the notion that if you have a case on the phone, it may interfere with the headphone plugging in. Definitely try taking the case off (if you have one on) to see if it makes any difference.
Have you tried any headphones that don't have the microphone ("normal" headsets that aren't specially intended to use with smartphones)? Its just odd that a AUX cable works, and headphones don't. The only thing I can think that can be different is the hardware and software differences that are associated with the microphone (buttons, etc.).
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Phone: AT&T HTC One (M8)
Tablet: Samsung Galaxy Tab Pro 8.4 (WiFi only)