As we all know, there is a "time and place for everything" for those with NORMAL common-sense, reason, logic, and intelligence. However, in a gym/health-club where you have a bunch of "juiced-to-the-gills", brain-cell destroyed, druggy, psychos runnin' loose...then any assumption of "normalcy" is out-the-window!
Having regularly practiced the martial-arts (ma) for over 40 years, I can ASSURE you that other trainees, observing those "pseudo macho tough guys" shadow boxing/fighting in front of the mirrors in the weight-training portion of a health club, would (of course!) think of such individuals as "show-offs", "nut-cases", etc.! This FACT holds particularly true for the "hot-chicks", working-out in the weight-room, whom you are trying to impress with your juvenile, moron-level, shadow boxing/fighting moves!!
Of course, many gyms/health-clubs with a weight-training section/room(s) ALSO have a SEPARATE section for ancillary ma training (e.g. heavy bags, speed bags, mirrors, ring, etc.). If not, you can always go off into the separate aerobics room and practice your shadow-fighting in SOLITUDE in front of the myriad of mirrors,etc.
Better yet, just practice your ma shadow boxing/fighting at HOME, the dojo/fight-club, outdoors, in solitude or with your ma training partners, etc. But ooooops, you wouldn't be able to SHOW-OFF in front of others would you...you fvckin', druggy, MORONS?!!