1
general::
Become embroiled in conflict, as in At the town meeting Kate and Steve locked horns over increasing the property tax. This expression alludes to how stags and bulls use their horns to fight one another. [First half of 1800s]
American Heritage Idioms
2
general::
Phrase(s): lock horns (with someone)
Fig. to get into an argument with someone. • Let’s settle this peacefully. I don’t want to lock horns with the boss. • The boss doesn’t want to lock horns either.
McGrawhill's American Idioms And Phrasal Verbs