Nelson, you seem to have misunderstood whatever it was that you were taught about stating objective facts. And no, you cannot say 'Lion has mane' - this is pidgin English. The only native English speakers would say 'Lion has mane' are two or three year olds. By the time we go to school, we have all learnt how to use articles properly! You have two options with your rabbit sentence. If you are describing general features of rabbits, you can use a plural subject with a plural object: "Rabbits have short tails." The other option is to use a singular subject with a definite article and a singular object. "The rabbit has a short tail." We use this convention when we are describing a whole species, as in 'The male lion has a mane, but the lioness does not'. This construction is more formal, and tends to be used in scientific and academic contexts. I hope that all makes sense.

Yep, the comments are all correct. You must use the plural form with rabbits/ tails when describing all of them as a general remark. However, specifically why… well, no one can say why, except it has always been that way. Maybe if you use it in singular, it specifically meant the one rabbit you saw. For example:" Rabbits have tails. Rabbits have only one tail". "Rabbits have two ears. That rabbit has only one ear". Poor rabbit…

a bunch of rabbits cannot have just one tail at all

the sentence are stating an objective fact, right? so why doesn't it just use the singular? such as rabbit has large front teeth... lion has mane Is it your custom?

one rabbit has one tail, but rabbits have tails