What was the motivation behind making a tryte equal to three trits? Seems counter-intuitive that a byte contains more combinations than a tryte—at least from a semantical perspective.
Trits are not very readable by humans, so English letters and a separator ('9') were used for combinations of 3 trits. Calling them "characters" would require to add "used in IOTA addresses" sometimes which is not convenient. Long story short, I decided to call them "trytes", that term wasn't used anywhere else anyway.
Regarding a byte being able to store more data, conventional computers operate with computer words, not bytes. Bytes don't longer matter much.
I didn't find any IOTA specific source to explain the choice to use trytes made of three trits.
Probably 27 being the number of all possible different combinations of 3 trits, (3^3), then 3 trits is the best choice if you want to use the letters in English alphabet (26), plus an additional character (9), to represent numbers in this notation.