Admonish – Put an end to an institution or a custom; To do away with things that have been long established or deeply rooted.
This word is used 6 times in Scripture: 3 times to Israel in their Masoretic Text Old Testament; and 3 times to the Body of Christ in the Gospel of Grace.
Abolish is a strong word, and signifies a complete removal, generally but not always by a summary act.
In Scripture, the specific institution that is abolished is death. The specific custom that is abolished is idolatry (religion / Christianity). The deeply rooted and long-established thing that is abolished is the enmity between God and mankind, and between gentiles and Israel.