I think this is a good concept, but activation is.. well not nice.
It should be a passive ability IMO. no hassles. It's not that OP.
I agree, although I don't think it should be passive. Just have it be a triggered ability, just like bioluminescence, phoenix, et al.
Degrade is active so it can be lobo'd, and so mutants can get it.
I might drop the anti-matter bit if I edit it again.
Just because something is "active" doesn't mean it should be an activated ability with a cost. Lobo removes phoenix and bioluminescence (see above), so if that is your only real concern, just make it a triggered ability that is activated with creature damage.