Hank Pym’s distaste for Howard Stark is evident from the first time they’re shown on screen together in Avengers: Endgame might explain why Pym hates Stark quite so much. Through the whole MCU Hank Pym is shown to be cantankerous and abrasive. While he has little patience for most people, Scott Lang included, his contempt for Howard Stark goes further than for anybody else.
In the opening flashback scene from 1989 at the start of Ant-Man, Hank Pym expresses his disdain for Tony's father, Howard Stark, and his attempts to replicate the Pym Particle. While this hatred is shown in context to Stark trying to replicate his research for the military when Pym has refused it to them, it seems to go deeper than that. Throughout his presence in the MCU, Hank Pym takes every opportunity to take shots at Howard’s name, but also for Tony based purely on his being a Stark, suggesting that there is an intense hatred of Starks on a moral basis.
According to the theory, an implication of the time travel in Avengers: Endgame secretly explains this deep-seated hatred Pym has for Stark. When the Avenger’s plans in 2012 fail to provide them with the Tesseract, they instead travel back to 1970’s Howard Stark visited the facility on the same day in 1970, it would not have been a great leap for him to decide that Howard had stolen his Particles as part of an attempt to copy his research, meaning that his later suspicion that someone might try to steal his work was based on a very valid concern.
During Ant-Man and The Wasp see antagonists that are trying to steal Pym’s research so that they can use it for nefarious purposes that Pym doesn’t approve of, his hatred for the Stark family clearly outstripped any other concerns he had. This all makes sense if he blames Stark for the one time previously that someone had successfully stolen some of his work.
Unfortunately, this theory does not entirely work with how Hank Pym’s hatred for Howard Stark must be based on other general ethical issues with how Stark conducts himself, but if not for the plot hole this would be a compelling answer to the root of the rivalry.
