>>34040519Ash is a paragon for the relationship of Pokemon. Where as in the TV series, being a "Pokemon Master" is largely a vague/abandoned concept, the film gave a direct answer, in that he wants to form a positive relationship with every creature. Ho-Oh cares about Ash because he lives true to such ideals, and Ho-Oh sees him as pure of heart, which is both explained in the film, and the game itself. In the same way that Ho-Oh wishes to protect and heal, that same "rainbow" is represented by Ash, hence why the golden feather is always apart of him.
The beast themselves share a similar ideal to Ho-Oh, in that they protect/guide the lands, but they're also both revered and feared (all shown during the Entei interaction, admittedly Raikou's appearance was frivolous and just an omen of things to come) so humans like Ash are the tool that Ho-Oh needs to bridge the gap between species, and shine "light" upon other humans of evil heart, just as Ho-Oh did in the Rainbow Hero illustrations, which Ash would then go on to (if not indirectly) purify the heart of Cross.
Marshadow is the being which "sets things right," and allows for the natural negativities of the world to proceed, observing them. If you think about it, Ho-Oh loves life so much to a point of effectively cheating it, creating the legendary beasts out of grief, and reviving Ash but Marshadow observed the grief of Ash and supported Cross's negativity, which is basically an anti-thesis to what Ho-Oh strives for. Frankly it's a missed opportunity to not have Marshadow observe the Spearow attack for this very reason.
What it means to exactly "be" a Rainbow Hero, and why Ho-Oh wishes to battle such a trainer beyond the formalities of respect between legendary and human is self-explanatory/up to interpretation, since there's little exposition a flying fire flamingo can deliver, unless you prefer the route of another telepathic legendary, but I find the silent legendaries to be a fresh breath of air.