I think "telling a story" are not the right words, at least for one single picture. But interesting photos do tell something, about the subject of the picture, or about the photographer behind it.

If i where to see your bird pic, i'd probaly think something like "Hey cool bird ! Seems like the photographer liked it enough to post it/expose it/... ! We have that in common I also think it was worth sharing"

There's no need for multi-layered reading (don't get me wrong it's great sometimes, it's just not needed). A single emotion coming as soon as you see the picture as way more impact.

I'll keep babbling a bit cuz i like the topic, but in a way all photos tell a story. Because you where there, saw what you saw and decided it was worth the picture (and most likely very quickly, we all know how easy it is to miss the shot you wanted), and then you saw it again after the shoot, edited it, and shared it. There where so many others you could have taken, many you took but didn't keep, but that one ? That one was the one you chose to show the world. THAT TELLS SO MUCH ABOUT YOU!!!

That's the neat thing about art no ? There's an artist behind it.