Wow, "su" means both "your" and "its"?
And "his" and "hers"
What in this sentence makes the cat feminine? "The cat drinks its milk."
Nothing. Both "el gato" and "la gata" work in this case.
would 'el gato bebe sus leche' be acceptable, since milk isn't really singular or plural? Or do we prefer to think of it as milk (pretty much) always being singular?
No, this would not be acceptable.
Why is es not acceptable for its?
"es" would be acceptable for "it's" (short for "it is"), not for "its" (denoting possession).
why is "sus" not accaptable?
"sus" would be for a plural object. It would be something like "The cat drinks its milks".
I thought cat was masculine and feminine.
Gato is masculine, Gata is feminine.
is there a difference between 'tu' and 'su'? what about 'tus' and 'sus'?
Tu = your (familiar); You'd use it when you're close to the person you're talking to.
Su = your (formal)/their/his/her; yes it has a lot of different meanings.