Argus Filch was a Squib and the caretaker of Hogwarts School of Witchcraft and Wizardry since around 1973.
Qualquer outra coisa é apenas especulação, mas o entendimento comum é o que a @Katey HW declarou nos comentários.
I always assumed it was because Dumbledore has a soft-spot for those who would be outcast from 'normal' wizard society; Hagrid is the most obvious example of this, but Remus Lupin is another. This is my read from the text, not a specific 'canon' answer