The following definitions from MEXICAN SLANG 101 © are selected and presented together as a sort of sociological commentary (or head scratching). Why does "father" mean "cool" and "mother" mean the opposite? Why would a Mexican woman call her son "daddy" and her husband "my son"? And the answer is: WHO KNOWS? It's worthy of conjecture, but mostly it's just Mexican Slang.
PADRE (PAH dray)
This is the closest equivalent to "cool" as in, "He's a really cool singer" (Es cantante muy padre.) Can also be used impersonally, like "Far out!," (¡Ay, que padre! ) The ultimate cool is Padrisimo (Pah DREES ee mo).
MADRE (MAH dray)
This is a very complex word in Mexico and produces a major amount of rich slang. Without getting into the sociology of it; although the concept of Motherhood is held sacred in Mexico, madre means worthless, failed, a mess. Una madre is something unimportant, a put-down; a desmadre is a total snafu. A madrazo is a heavy blow or jolt, a madreador or madrino is a bar bouncer, hit man, or goon. Partir la madre is to smash, destroy, or bust something. Tu madre is the equivalent of "yo mama". (And the instant reply is, la tuya, essentially, "No, YOUR mama.")
Exceptions to all this maternal negativity are a todo madre, which means done right, superlative, done up brown, the whole nine yards; and no tiene madre--if something "has no mother" it is absolutely the coolest. However, and to illustrate the importance of context in such elemental slang, El no tiene madre can also mean having no shame, so to say someone has poca madre (not much mother) means they're a jerk. Poca abuela (not much grandmother) avoids the crude use of the word madre). .")
Me vale madre, is a classic of Mexican badassery, frequently seen on caps, shirts, and biker jackets. It literally means "It makes mother to me." but is a direct equivalent to English expressions such as "I don't give a damn." or "Who gives a rat's ass?" A MUST phrase for slangstas. Some neat words in that particular constellation include, valemadrista (somebody who doesn't give a shit), valemadrismo (a generally apathetic or "who cares" attitude) and the concept that a person has an actitud muy vale.
Madre used like this is not considered polite, so there are euphemisms like a todo M (ah toe doe AIM ay) or a la M like we would say, "the M word". There is also drema, with the slyly syllables reversed, and the even more scrambled la ingada chadre.
With that kind of weight behind the words for "father" and "mother", it's not surprising that people actually call their parents (los padres or los viejos) mamá and papá. The short forms, mami (pronounced just like "mommy") and papi (rhymes with "poppy") are used by children, but also affectionately applied by adults to both children and spouses.
In fact, in a further twist on maternal/paternal nomenclature, mamacita and papacito are not affectionate terms for parents, but what lovers call each other (or would-be lovers, much as Americans might say, "Hey pretty momma" to hit on somebody). When a grown woman speaks of mi papi it's assumed she's not talking about her father (generally obvious from context.)
MIJO (MEE hoe)
Mi'ijo is a contraction of Mi hijo--"my son"--is like "sonny" used in addressing younger boys. Affectionate use of mijo between friends and peers is a major Mexicanism. Mija (MEE hah) is used to address women, the same as mijo with males.