On the excellent series The Toys That Made Us, former Mattel marketing VP Paul Cleveland explains why He-Man rides around on a giant green cat. Here's the story from Wikipedia but watching him tell it above is much more entertaining:
…While the decision was made for He-Man to have some sort of vehicle, they no longer had the budget to be able to produce one; the decision was then made to repurpose a tiger from the Big Jim toy line. The tiger was, however, not the same scale as the He-Man figure, and compared to He-Man, was about the size of a horse. Cleveland, however, insisted it to be used, even after artist Tony Guerrero made a green version in an attempt to discourage Cleveland, who instead suggested simply putting a saddle on it, which resulted in Battle Cat's final design
(via @ponettplus, thanks UPSO!)
