Remember that Endeavor/Enji was looking to create the perfect child, one who had both the ice and fire quirks. Therefore, his last child, Shouto, had the perfect balance of fire and ice. (thus the mistreatment when younger and the harsh training by his father)
Dabi, as the oldest child/second oldest, could have very well been forsaken and have taken a more negative reaction to his father's treatment. Also because he has mainly the fire quirk, he could also have been hated by his mom (because he reminded her of Enji). Compared to the other two siblings who had mainly the ice quirk of their mother.
Endeavor was mos tlikely disappointed that Dabi only had the fire quirk and possibly just tossed him aside....
I feel like this confirms Dabi being Endeavers son, like tf <u> I feel like he was a 'forgotton' child or something, or someone who didn't recieve his quirk at a young age, so Endeaver didn't really pay attention to him. ,-,