One possible reason why King Cold might've preferred Frieza is that he seemed to accomplish more than Cooler, even though the older sibling proves stronger during their lifetimes. RELATED: 8 Anime Video Game Spinoffs That Are Actually Worth Your Time The Accomplishments of Frieza vs. Yet when King Cold retired from his planet trade organization - shown in Dragon Ball Super: Broly - he announced his younger son Frieza as his successor and gave him the keys, rather than Cooler. Cold also helps Frieza get revenge on Earth, while offering Cooler little to no help - though, bizarrely, Cooler came far closer to killing Goku and friends than his brother and father did. However, King Cold goes out of his way to rebuild Frieza while allowing Cooler to return as Metal Cooler on his own through some Lovecraftian machines. There are obvious continuity issues with that placement (Goku wasn't on Earth at the time), but this establishes that Cold lost both of his sons in quick succession.

The film should take place immediately after the Frieza Saga but before King Cold's arrival on Earth, due in part to Gohan's hairstyle and Cooler believing that Goku killed Frieza rather than Frieza being rebuilt by his father and slain by Trunks. Due to Cooler's Revenge's complicated place in Dragon Ball Z canon, it's hard to determine how much of what Cooler said should be taken into consideration.