The familiar from find familiar isn't an ongoing magical effect to be dispelled. When you cast the spell (with a duration of instantaneous), the following occurs (from the spell's text):
You gain the service of a familiar, a spirit that takes an animal form you choose... it is a celestial, fey, or fiend (your choice) instead of a beast.
The spell doesn't create the familiar, per se. Rather, the familiar is a spirit whose service you instantaneously gain when you cast the spell. So the familiar isn't a spell effect.
In addition, the spell's duration of instantaneous indicates that there is no ongoing effect to be dispelled (from the rules on spell duration):
Many spells are instantaneous. The spell harms, heals, creates, or alters a creature or an object in a way that can't be dispelled, because its magic exists only for an instant.
So the familiar can't be dispelled using dispel magic.
For more details on dispelling magical effects, see this related question.