I am doing some Latin exercises and the sentences are given as the following (by Rosetta Stone):
Puer plus lactis habet quam vir.
Femina plures canes habet quam vir.
In the first case ("more milk") the object is in the genitive, but in the second case ("more dogs") the object is in the accusative. Why would these two parallel sentences differ in this way?
Asteroides's answer is spot-on, but since the comments express confusion with it, I'll try explaining it a different way.
Much like you wouldn't say *"the boy has more milks" in English, you wouldn't say *plura lacta in Latin. (You could perhaps use the plural if you wanted to talk about a café with many different types of milk, but it still sounds strange to me.)
The problem is, the adjective plurēs/plura doesn't have any singular forms, since semantically it's always referring to a large amount of something. So you can't say *plus lac, with an adjective, either.
So Latin uses a different construction in this case: the neuter noun plus with a genitive of quantity. You can think of it as "a larger amount": the boy has "a larger amount of milk".
For canis, though, there's no reason to say "a larger amount": there's a plural canēs "dogs", so you can just modify this with an adjective to get plurēs canēs, "more dogs".
This is the standard way to talk about "more" of a count noun, though you can also use plus with a genitive if you really want to: plus hostium "a larger amount of enemies".
The form plūs can be used as an adverb or as a neuter noun, but not as an adjective. Only its plural forms (such as plūrēs) are used adjectivally. So the difference between your sentences is because milk (lac, lactis) is singular but dogs (canēs) is plural.
The adverb has the invariable form plūs (Latin adverbs are invariable as a rule and quite often have the form of neuter singular nouns).
The adjective has the plural forms plūrēs, plūra, plūrium, plūribus. It agrees in gender and case with a plural noun, which takes the usual case for its function in the sentence, to form an expression meaning "more [plural noun]". This is the usage found in plūrēs canēs.
The neuter noun plūs has the singular forms plūs, plūris, plūre. It is "defective" (unattested) in the dative singular. The neuter noun plūs is used with a noun in the "partitive genitive" to form an expression meaning "more [singular or plural noun]". This is the usage found in plūs lactis.
Therefore, plūs lactis is the only way to say "more milk" using plūs. The whole phrase plūs lactis acts as an object, and the head of this phrase is the neuter noun plūs, which is accusative. The genitive lactis is not inflected any further for the case of the surrounding phrase, because that isn't possible in Latin: genitives don't agree in case with the nouns that they modify.
"More dogs" in the accusative could and generally would be plūrēs canēs. Because "dogs" is plural, there is the option of using the construction with the plural adjective plūrēs. Since plūrēs is an adjective, it agrees with the head noun canēs, and both are accusative plural.
I'm not sure whether plūs canum (with a neuter noun plūs and a plural genitive noun canum) would be likely. I think it is usual to use adjective forms like plūrēs to express "more" in combination with plural nouns, but I have seen a few examples of plūs with a plural genitive.
