Yea i had a friend that said this same thing, called him stupid. lol You can play her as suport if you want, you can play anyone as support and justify their kit in one way or another. Yauso has cc and a wall to protect his adc from auto attacks and abilities. Ori has a speed boost, a slow, a shield, cc and damage, she can support. Syndra has a stun and a slow, she can support. Quinn has a ability that gives vision, she can blind the enemy adc and vault of them to stop channels.
You can justify anyone as a support, the point with Kalista is that she is designed to be an adc. Her passive, her q, her w and her e all allow her to be very strong alone. There is no reason to play her as support, on a support budget when she is stronger than most adcs without her ult. Her ult is just icing on the cake that allows for her to tell her support when to engage. It allows other champions such as galio to be a support now. You toss him into the team, he ults, ur ori mid ults, you win.
So, play her as support if you want, but your argument for her being a support is no more or less valid than for quinn being a support or braum being a top laner. There are justifications for everything, that doesn't mean that is where they are best suited.