Why do we use the phrase Across the pond to refer to the opposite side of the Atlantic Ocean? Considering the size of the Atlantic Ocean is vast, is it suggesting the ocean is only a small hindrance? Considering that in the modern world it has become easier to communicate and travel?
This question on Linguistics Stack Exchange addresses this, asking if mother and father are true antonyms. I'll quote the accepted answer, written by robert, which basically boils down to "Technically no, but sometimes yes."
Mother is not the antonym of father. They are co-hyponyms because they are both a kind of parent - and parent is the hypernym of mother and father.
Antonymy is the relation that holds between parent and child. So by extension the antonym of mother could be said to be child.
EDIT: After reading hippietrail's answer, I somewhat changed my opinion. If one considers two words to be antonyms already if just one of their semantic features is replaced with the opposite then mother (female parent) and father (male parent) can be said to be antonyms. However, I feel that it might make sense to reserve antonymy for complete negation or oppositeness, and describe the relation between mother and father as hyponymy.
One thing to keep in mind is that language textbooks are often geared toward students who are at a very basic level of that language. For someone who is just beginning to learning English, framing words like mother and father or son and daughter as opposites is a simplification that helps students learn the proper use of those terms. In a simplified way, it makes sense: a mother is a parent who is not a father, and a father is a parent who is not a mother; a son is a child who is not a daughter, and a daughter is a child who is not a son.
This simplification serves the same purpose as the simplification often taught to children just beginning to learn division that even numbers can be divided by two and odd numbers can't. Later on, when they're more advanced, the students will learn that odd numbers can be divided by two; it's just that doing so doesn't result in a whole number. At a more advanced stage, students will learn that words like father and mother aren't true opposites like hot and cold are, but at the moment, that terminology suffices.
Two sources (for boil the sea) predate Carroll's 1871 quote. The first is unambiguously about heat:
If he utters a tone of dissent I will boil the sea dry
The Asiatic Journal and Monthly Miscellany, Volume 32 (1840) p. 61 "The Dragon King's Daughter" (short story).
The second is less clear, in that it could be metaphorical:
Hail to our master! He whose sway,
Hell’s terrified realms obey.
In the fell ingredients throw!9
Now our charm has wrought its woe!
Thunders burst and boil the sea!
Dance about, with witches glee!
Let our timbrels shake the air!
Our delight is man’s despair!
The Mountain Sylph (an opera John Barnett, libretto by Thomas James Thackeray, 1834)
The figurative "boiling" is quite common, and old, which doesn't help track down a more literal meaning, but may have influenced later origins of a phrase meant literally. For example Edgar Allan Poe "A descent into the Maelström" (1841):
Here the vast bed of the waters... burst suddenly into phrensied convulsion—heaving, boiling
Alexander Pope's 1726 translation of Homer's Odyssey also uses this metaphorical sense:
Beneath, Charybdis holds her boist'rous reign
'Midst roaring whirlpools, and absorbs the main;
Thrice in her gulfs the boiling seas subside