Quinolones are bactericidal and tetracyclines bacteriostatic. As a general rule, you don't combine these opposing acting groups, so only cidic+cidic or static+static. For specific combinations it might be different, but it's an exception rather than rule in that case (since the general rule is an oversimplification of complex mechanisms of AB pharmacodynamics). However, as a senior medical student answering this question on a test I wouldn't say their action is antagonistic (since pharmacological antagonism means opposing effect on the same receptor), andI don't think a concurrent application in clinical setting would be appropriate. Maybe you could call that 'antagonist action' on a general level. But sounds like a misnomer and could just yield more confusion.
I suggest further readings in the links below.
EDIT: a previous discussion on RG https://www.researchgate.net/post/Why_can_we_not_give_Bacteriocidal_and_Bacteriostatic_antibiotics_together