I'm trying to find the connection between Psycho Shift and Bird-Like pokemon. By level up, the only pokemon that aren't flying type that learn it by LvL up are the ones with Levitate. Even then, Latias, Latios, and Cresselia look kinda like Bird-Dragon-Jets and a Moon-Duck. By breeding the only non-flying is togepi, which evolves into a flying type. In old gens, Murkrow Line got it too. Deoxys disrupts the pattern, but whatever. It's Japanese name translates to Psycho Shift, so no Splash = Hop revelation... I need help
I'm not convinced that there's an inherent association with bird Pokemon - just that those Pokemon that get the move happen to be bird-like. "Suggestion" is an odd word in this context but throws up associations with illusion and telepathy. Most of the Pokemon that get Psycho Shift tend to be ones which use their psychic (or Dark, Fairy, etc) powers for these purposes rather than manipulating the elements, and learn similar moves that mess with the opponent's stability or perceptions.
Hoothoot and Noctowl have always learned tricky Psychic moves of that sort - they're honorary Psychic-types (there was a discussion about Pokemon of this nature a while back possibly on a different thread). Latias and Latios both have an affinity with perception and illusory, suggestion-related moves, as do Cresselia and G-Articuno. The same goes for Abra, Sigilyph, Indeedee, Woobat, Murkrow, and Spinda - albeit with some of those you have to really squint, but it's just enough of a connection in most cases. Murkrow in particular is often found in dark, shadowy caves and forests and though none of its Pokedex entries link it with illusory abilities, it's not hard to imagine it using these sorts of powers, particularly as it gets a lot of moves like Haze, Night Shade, Mean Look, and Confuse Ray.
Natu and Xatu are associated with premonition and otherworldly second sight, so it's not a total stretch to link that with "the psychic power of suggestion". Other Psychic mons, such as Hypno and Mr. Mime, don't have that association as they have other kinds of psi power. Quite why all four Deoxys forms get it is puzzling as it seems a move more suited to the Defence form alone, but all four formes learn moves like Recover and Night Shade so it's not a total stretch.
Togepi's the really odd one imo, though much like Hoothoot it does learn a lot of tricky Psychic moves like Extrasensory and Telekinesis. I guess "suggestion" in this case is similar to the intuitive power utilised through Metronome - which Togepi is heavily associated with - and through the suggestive power of moves like Tail Whip and Charm.
Though I'm surprised that the Ralts line doesn't get the move, nor Audino - they're strongly linked to empathic powers of that nature.