Taking what was said earlier. How do you counter and kill something with 60" move (using print) that moves around and halves a bunch of movement and TMM and then disappears around a rock. They effect applies till the start of a new phase, they don't need to stay in line of sight. So you run around, wipe out all the TMM on things that moved quick and go hide. During combat phase they are no longer demoralized but they still have super reduced TMM.
There's a few things to reply to.
Sportsmanship: We might have to go ahead and disagree as to whether someone using a 60" move to maximize the ability to exploit Antagonizer is being a good sport. If you can't rule these sorts of things out from the "good sportsmanship" code of conduct, then you might have to start looking at removing some of the optional rules you play with. Alpha Strike isn't written to be a competitive game.. if you want to play it that way you really shouldn't be using unbalanced optional expansions to the rules like SPAs and Sprint anyway.
Current state of Antagonizer: Remember that even with a 60" move you can't deny the opponent control of large swathes of his army. Antagonizer is actively triggered at any point during your own move, and only affects units within 6" of the Antagonizer
at that moment. Furthermore, if those antagonized units begin any phase (movement, or combat) more than 24" away from the antagonizer or without LOS to it (you hid behind a rock) the SPA's effect immediately ends.
Current state of Demoralizer: Demoralized wears off the same way as antagonized. (You seem to be under the mistaken impression that hiding out of LOS is going to allow the Demoralized debuff to last into the combat phase) If you swept around to TMM nerf half the opponent's force and still stay within 24" of all nerfed units and inside their LOS so that the debuff doesn't expire... it ain't gonna live through the round to ever do it again. Even a +1tn won't save it from that much concentrated hate (and artillery will ignore it anyway). And besides, demoralized targets can shoot at everything other than the demoralizer at no penalty (unlike Antagonized units, which must shoot at their debuff-er...)
"How do you counter and kill [a fast Demoralizer]...": If you moved it late, I've already got full value of my MV on the affected units and all you're doing is lowering their TMM by 1-2. And if you hide out of LOS, not even that as the effect immediately wears off when Combat phase begins and your Demoralizer is >24" away or out of LOS...
OTOH if you moved the Demoralizer early in the phase, before I moved the affected units, they'll mostly just go into whatever cover is still available, or even to stationary for the firing bonus if already in cover. However something will be able, even if my entire army is at 1/2 MV, to achieve LOS to wherever you hid. And artillery will guarantee your demoralizer doesn't see another round. It'll only take 1 or 2 hits to knock out anything that can go 60". And since LOS is reciprocal, if you Demoralize early and go break LOS then my TMM will be restored when you're shooting at me in the combat phase...