Hence the problem with colloquial naming traditions. We arbitrarily decide what is an isn't a moth based on our feeling at the time.
Is a chihuahua a wolf? Most would say no. Did chiahuahuas evolve from a wolf-like ancestor? Most likely. We will say that chihuahuas and wolves are still dogs, but when did those wolves stop being wolves and become chihuahuas? That dividing line would also be an arbitrary one.
The system that science has settled on is cladistics, and in that system you never evolve out of your clade. This differs from the colloquial method where species are arbitrarily assigned to different groups based on shifting notions of what is or isn't indicative of a group.
Yes, that's one of the reasons we have terms like Heterocera when it comes to scientific nomenclature, instead of simply making do with 'moth', so that we can have a learly defined phylogenetic concept independent of people's arbitrary impressions of what a thing should be classified as.
But I don't think using this sort of argument helps when someone is protesting that a sloth is never seen to turn into a turtle. Saying that 'the descendants of sloths will always be sloths' isn't true - it's equivocating between a common name which we wouldn't apply to something that looks substantially different to a sloth, and the phylogenetic concept 'Folivora'.
amp1022's problem seems to be that he thinks the transition from fish to ostrich is supposed to happen in an afternoon and only involve one animal. Trying to explain phylogenetic nomenclature is more like to confuse than to help, at this point.