"promote animosity" is correct and can be used in written English to describe actions or behaviors that incite hostility or dislike between people or groups.
Example: The politician's divisive rhetoric only serves to promote animosity among citizens, instead of promoting unity.
Parties "distract the public councils," "enfeeble the public administration," "agitate the community," "promote ill-founded jealousies and false alarms," kindle "animosity" and occasionally foment riot and insurrection.
As a result, he says, PA consultants now feel little animosity towards colleagues who think they can do better with a competitor.Besides solving the problem of mixing old and new, PA has also tried to promote co-operation.
" Promote, promote, promote!
It's an ironic claim coming from a man whose network has profited for years from promoting racial discord, only to see that very animosity torpedo his political party and ensnare their media megaphone.
It was made in obscurity somewhere in Southern California and promoted by a network of right-wing Christians with a history of animosity toward Muslims.
LOS ANGELES — The film that set off violence across North Africa was made in obscurity somewhere in the sprawl of Southern California, and promoted by a network of right-wing Christians with a history of animosity directed toward Muslims.
Armitage also promoted the idea that the decision to send Shackleton home on the relief ship arose from Scott's animosity rather than Shackleton's physical breakdown.
Kalanick had promoted the idea of internal competition, with different teams battling against one another on the same project, which led to secrecy, lack of coöperation, and animosity among employees.
