Why do passenger embark on the left side of an aircraft?
Because the cavewoman who invented the log-canoe was right-handed?
Note: I arrived at this answer by looking at a kind of etymology of the terms starboard & port but that's incidental. The answer to this question happened to be contained in an answer to a rather different question. Some groups of aviators may have dropped the archaic terms while still being subject to a continuation of an archaic habit/convention.
People get on the left side of a jet airplane because Vikings (etc) steered their wooden boats with a steering board (hence starboard?) held in their dominant right-hand.
Since it was inconvenient to have your steering apparatus wedged against a quayside (or earthen bank) they docked at the port along their left side and therefore loaded and unloaded on the left.
Farhan's comment leads you to this answer in English.se which I reproduce here for convenience
Excerpt from trivia on the Navy website:
Port and starboard Port and starboard are shipboard terms for left and
right, respectively. Confusing those two could cause a ship wreck. In
Old England, the starboard was the steering paddle or rudder, and
ships were always steered from the right side on the back of the
vessel. Larboard referred to the left side, the side on which the ship
was loaded. So how did larboard become port? Shouted over the noise of
the wind and the waves, larboard and starboard sounded too much alike.
The word port means the opening in the "left" side of the ship from
which cargo was unloaded. Sailors eventually started using the term to
refer to that side of the ship. Use of the term "port" was officially
adopted by the U.S. Navy by General Order, 18 February 1846.
So it's a historical convention, many arbitrary choices are of this sort. Pioneers of a new form of transport adopt the terms (port, startboard) and habits of more ancient forms of transport.
Ironically, since aircraft became able to carry substantial non-human cargo, the cargo entry has moved to the other side to reduce the chances of crushing the human cargo with the non-human cargo. Presumably also because having lots of large holes all in one side may be structurally disadvantageous.