I always thought 1/4 length was easier because you can make one easily from 1/1 length
by breaking in half exactly two times.
And then you have 4, so more economic too.

A dipole is made from two quarterwaves. An odd quarterwave is
easy to match to. Any other length needs a matching network
of some kind. Gain comes about from directing the RF in
some directions. This can be one direction like a beam,
or omnidirectional with something more complicated then a
simple quarterwave antenna.

Tell your instructor he needs some more instruction.
(Electronics books are in 621 at the library)