Not really sure why they have that option. Its like giving the keys to the house to a stranger.
You just answered your own question.
You should be extremely weary and cautious of any service that asks you for private keys. That's like a member on the forums here asking you for your account password to verify that you're a real member...
Looking at IDEX, do you know what raises red flags immediately for me? The part where it says:
Learn how you get paid to trade on IDEX!
Yeah, I wouldn't touch that site with a 10-foot pole.