I think that this is not pure antonymy. If it's still antonymy, do linguists have a separate term for this type of semantic relationship?
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.
I disagree with hippietrail's answer as I have not seen any dictionaries which describe this type of relationship as antonymy. For example: father, père. In Merriam-webster we have descendant as antonym, and in TLFi enfant. As such, I don't think considering these types of words as antonyms is a common point of view.
In Semantics (1977, pp. 279—280), John Lyons calls this relationship converseness:
To be distinguished from antonymy and complementarity is converseness*, exemplified by pairs like 'husband' : 'wife' (which may be regarded as two-place predicates). The sentence 'X is the husband of Y' express a proposition whose converse is expressed by 'X is the wife of Y' (cf. 6.3).
Converse relations between lexemes which may be used as two-place predicative expressions are especially common in areas of the vocabulary having to do with reciprocal social roles ('doctor' : 'patient', 'master'/'mistress' : 'servant') and kinship relations ('father' : 'mother','son' : 'daughter' etc.) <...>
But in my opinion it's not applicable for lion/lioness, tiger/tigress so I don't know how to call this kind of relationship.
Yes they are antonyms. That doesn't affect whether they may have other, possibly even overlapping or seemingly contradictory relationships, such as being co-hyponyms.
Antonyms are two words which are opposites. That seems pretty simple. But in fact you have to think about what "opposite" means, and what it means for words in particular.
In the end it comes down to semantics like so many other things, and people will surely come up with multiple analyses.
- Antonyms can be adjectives naming properties: short vs long.
- They can be abstract nouns naming properties: shortness vs length.
If a property can possess a value along a scale then generally values toward each end of the scale are seen as opposites.
Then there are properties which can have one of two values, which can of course be analysed as a special case of the previous.
I'm sure some people analyse "male" and "female" to be antonyms, and people who would strongly refute it. They can certainly be argued against semantically.
If two words are nouns then they need refer to objects having one property which has "opposing" values. Some nouns have more than one property capable of this. Others have none.