In other words, (i) states that if (A) then (B), (ii) states that if (B) then (C), and (iii) states that (A) = (C). The problem is that (i) and (ii) imply that if (A) then (C), not (A) = (C). If (A) determines (B) and (B) determines (C), then Euthyphro cannot claim that (A) and (C) are one and the same.
We should note that it is possible that (A) and (C) refer to the same deeds. If everything that is divinely approved gets approved by the gods (which seems almost irrefutable) and if everything that gets approved by the gods is holy, then what is holy and what is divinely approved of are the same things. The point Plato is making is not that (A) and (C) necessarily refer to different things, but that even if they do refer to the same things, they do not have the same meaning. For instance, every creature that has a heart also has a kidney, but "creature with a heart" and "creature with a kidney" do not mean the same thing, and cannot be said to be equivalent even if they refer to exactly the same things. Similarly, Plato wants to suggest, what is holy and what is approved of by the gods do not mean the same thing and cannot be said by Euthyphro to be equivalent.
This argument is a very forceful move against the idea of morality as being determined solely by some kind of divine authority. For example, in the Judeo- Christian tradition, we might be tempted to say that what is good is good because God says it's good, but we have not made ourselves sufficiently clear. Does God approve of it because it is good, or is it good because God approves of it? And, following Plato's argument, does this mean that what is good and what God approves of are two different things that cannot be equated? Because of arguments like this one, modern ethical theory tries to ground moral responsibility in our own autonomy rather than in God, regardless of whether the philosopher in question believes in God.