I'm bird phobic. I love to watch them from a window, but if they fly towards it I have to run away.
I have to cross the street if there are pigeons scoffing food someone's dropped, I once had to get a security guard to chase a seagull from the roof of my car in a supermarket car park, I fainted in a gloomy junk shop when a macaw on a perch squawked and flapped about 2' away from me (because the shop was very dark, I hadn't noticed the flappy fucker) and when I had a cat that brought in live starlings I had to get a neighbour (and on one occasion, some policemen who happened to be along my road) to remove them before I can go in.
I had to have CBT some years ago, because it had got so bad that I thought I was going to have to give up driving. If a bird flew towards my windscreen, it was virtually impossible for me to resist the urge to duck and cover my face with my arms. It's much more manageable now, a little blackcap flew into our sitting room the other day and I quite calmly walked into the kitchen and shut the door behind me, while telling (not asking!) DP to deal with it.
Oddly, I've never been scared of ducks or chickens. They just don't freak me out for some reason.
I'm also quite scared of heights, despite having been fearless as a child and young adult. I stay a long way from any cliff edges and couldn't stay somewhere like the Shard, where you're up high and the walls are entirely made of glass.
I think being scared of heights is pretty rational though, all things considered.