It's pretty much confirmed that Mystik, the foster mother of Tae Joon Park (Crypto) and Mila Alexander is the same person as Katerina Ticacek Nox, the mother of Alexander Nox (Caustic); Caustic and Crypto are stepbrothers. With this in mind there is a lot of deeper meaning behind the relationship between Caustic and Crypto.
The Jealousy Theory
From their dialogue interactions in-game, as well as the S5 Quest it is clear that Caustic is targeting Crypto. His said reason is that he wants him to stay away from Wattson; he is a "distraction to her greatness". But I think it's much more than that. My theory is that when Mystik (Caustic's mother) adopted Crypto, Crypto got more attention from her than Caustic did to the point where Caustic felt she loved her foster children more than her actual son. Caustic became jealous and this jealousy set out his destiny as a sociopathic scientist. Maybe he wasn't obsessed with scientific discovery, rather he went to extreme lengths to finally make his mother proud of him. But it all peaked when his own mother claimed her son was dead, as if she didn't care. This is what darkened him inside and why he, after learning Crypto's identity, has a grudge on him. In Caustic's eyes, Crypto is the reason his life is the way it is and was. We also see this extreme hatred in one particular dialogue interaction where Caustic calls Crypto a "gutter rat". The so called "racial slur" actually has more meaning behind it, where Caustic is mocking Crypto's sad origin by calling him street trash; Crypto's parents abandoned him and he lived on the streets as a child before being adopted.