The haggadah (several copies that I've looked at, so I'm assuming this is universal?) tells us when eating certain foods at the seder to recline or lean to the left. I understand why we lean (the haggadah tells us that), but why the left in particular? Is this because of historical practice (maybe couches were asymmetrical)? Is there a symbolic reason? Some other explanation?
I'm asking why the haggadah has this instruction; while later interpretations of what it means may be interesting, that's not my question.
The Talmud says (Pesachim 108a) that leaning on one's right is not considered Heseba (leaning). Rashbam explains this is because you have to eat with your right hand. (For lefties this would be the opposite. -- Me'iri) It seems this is because you lie on your side on your left, leaving your right hand available for eating with, unlike your left hand which is being lain upon.
The Talmud also says to not lean on the right lest your windpipe catch the food instead of your esophagus and you choke. I cannot comment on the specific anatomical details of why this is so. (For lefties then this would be the same. -- Me'iri) Note though, that some (including Rashi) interpret this passage as explaining that one shouldn't lean on one's back lest one choke, which is an earlier statement of the gemara.
the right bronchus is more vertical than the left bronchus, so it is easier for food to accidentally go into the right lung and cause choking. That is the anatomical reason behind why leaning left helps you choke less.