Alex told Kara to go to her alien side. That may have been the wrong answer, at least if they ever work out who Reign is.
I've gone back and forth on the advice that Alex told Kara. My first thought, and the one that I still favor, is that it was the right advice. Humanity is generally a strength but, in a battle, it can also be a weakness. Alex knows this and only wanted to give Kara the best odds of survival. We actually witnessed this when Kara's humanity actually did distract her during her fight with Reign.
On the other hand, her advice could cause Kara more confusion going forward. Here we have Kara, who is already questioning her humanity and we have Alex, who is an important guide to Kara, telling her that survival depends on shedding her humanity. Then, we see Kara allowing her humanity to distract her in the fight, which ultimately allowed Reign to get the upper hand. Will the combination of these two events throw her over the edge of humanity and impact how she approaches future events in her life?