The phrase "a deep antagonism" is correct and usable in written English.
It can be used to describe a strong and intense feeling of hostility or opposition between individuals or groups.
Example: "The negotiations broke down due to a deep antagonism between the two parties, making it impossible to reach an agreement."
Alternatives: "a profound hostility" or "a strong animosity."
So do these recent stories reflect a deeper antagonism between Britain's commercial food producers and their amateur city cousins, who buy organic when they can? Green groups such as the Transition Network have become energetic advocates of locally grown and sourced produce.
But a section of the community has declared its deep antagonism toward the new arrivals.
McKenzie's deep antagonism toward land monopolists was rooted in his boyhood in Scotland, where he witnessed the dispossession of small farmers by Highland landlords.
The deep antagonism on the issue has left it unclear how or even whether senators will find common ground as the nation confronts the prospect of its first recession in 11 years.
He made no effort to conceal his deep antagonism to Oslo, denouncing it as incompatible with Israel's right to security and with the historic right of the Jewish people to the whole land of Israel.
[C1.] Before Close Vote on Trade, Intense Deal-Making The cliffhanger House vote to approve the Central America Free Trade Agreement was one of the most wrenching in Congress this year, and it highlighted the messy compromises that were necessary to overcome deep antagonism in many quarters toward trade-opening agreements.
While they are members of international indigenous peoples' organizations and consider themselves akin to the Indians and the Inuit of the Americas, they have not experienced the same historic levels of violence and repression, do not feel the kind of deep antagonism that some native peoples do toward colonizers and have been less demanding in pressing their cause.
As we will see, however, his deep antagonism to probability combined with his passionate love affair with boldness was both a blessing and a curse.
Whether explicitly or by omission during the Oregon occupation, Republican candidates have demonstrated their deep antagonism toward environmental protection, said Kieran Suckling, executive director of the Center for Biological Diversity.
