In third grade I learned that Gerald Ford was the only president who was never elected because he took office after Nixon’s resignation and wasn’t re-elected. Millard Fillmore however, succeeded Taylor after his death and also wasn’t re-elected. Why isn’t he considered the same as Ford? Was it because the whigs nominated him for VP rather than being chosen by the president?
The distinction here is to what office these men were elected. Gerald Ford is the only person to have served as VP and President without being elected to one or the other office (that is, no electoral votes were cast for him as either president or VP).
He wasn't "never elected" -- he was a Republican member of the House of Representatives from 1949-1973, and the House minority leader from 1965-73, so he stood for election every two years during that time (1948, 1950, 1952, ... )
Fillmore, in contrast, was elected to the office of the vice presidency (by 1848, electors were voting for both offices).