Conifold is right to draw attention to the fact it involves an equivocation of the copula 'is' for starters.
Let's look at the argument with enthymemes and some clarification
P1 The opposite of 'normal' IS-BY-DEFINITION abnormal. (a priori claim)
P2 'Sleeping' IS-BY-FREQUENCY normal. (a posteriori claim)
E1 [The 'opposite' of sleeping IS-BY-DEFINITION being awake.] (a priori claim)
C If sleeping is normal, and then it's opposite being awake must have the opposite of its properties. (a priori claim)
But in fact, the property of normality applied to either state is a question of frequency, that is to say, it is an empirical fact that is normal for humans to sleep and to be awake. The properties aren't analogues.
But the equivocation only undermines the rule for drawing the conclusion, which itself would seem to be a false analogy. That is to reason that both terms have opposites means that their opposites share the same properties.
Let's look at another example:
P1. Not in the kitchen is the opposite of being in the kitchen. (a priori claim)
P2. Socrates IS-BY-EXPERIENCE in the kitchen. (a posteriori claim)
E1. [Socrates IS-BY-DEFINITION the opposite of his wife.] (a priori claim)
C. Therefore, Socrates's wife is not in the kitchen.
Here again, the copula is used in two different senses, and we cannot presume that the location of Socrates's wife is the opposite of his, because men and women are in a sense paired in a marriage.
It's a false analogy to presume that two different entities that are opposites have opposite properties.
You've added a second example, and stated correctly, it's not a fallacy.
P1. Whatever is not normal IS-BY-DEFINITION abnormal. (a priori claim)
P2. Being Asian IS-BY-FREQUENCY normal (say, in Asia). (a posteriori claim)
E1. [Among a mixed group of Asians and Caucasians, if you are not Asian, you ARE-BY-DEFINITION Caucasian and vice versa.] (a priori claim)
C. Being a Caucasian (say, in Asia) IS-BY-FREQUENCY abnormal. (a priori claim).
In this case, the argument is correctly analogical because the frequency of two groups DO have opposite properties. In this case, the majority population by definition has the opposite property of the minority population.