"put an end to, do away with," mid-15c., from Old French aboliss-, present participle stem of abolir "to abolish" (15c.), from Latin abolere "destroy, efface, annihilate; cause to die out, retard the growth of," which is perhaps from ab "off, away from" (see ab-) + the second element of adolere "to grow, magnify" (and formed as an opposite to that word), from PIE *ol-eye-, causative of root *al- (2) "to grow, nourish," and perhaps formed as an antonym to adolere.
But the Latin word rather could be from a root in common with Greek ollymi, apollymi "destroy." Tucker writes that there has been a confusion of forms in Latin, based on similar roots, one meaning "to grow," the other "to destroy." Now generally used of institutions, customs, etc.; application to persons and concrete objects has long been obsolete. Related: Abolished; abolishing.
Abolish is a strong word, and signifies a complete removal, generally but not always by a summary act. It is the word specially used in connection with things that have been long established or deeply rooted, as an institution or a custom : as to abolish slavery or polygamy. [Century Dictionary, 1900]