Why are Class C IP addresses preferred in private networks?
Solution 1:
I don't think they're preferred. I've seen plenty of networks using RFC1918 class A, B, and C addressing schemes. Use the class that suits your needs:
How many subnets do you need?
How many hosts per subnet do you need?
What routing needs do you have to route traffic between subnets?
Do you anticipate having a large number of hosts per subnet and want to reduce the size of your broadcast domains?
Solution 2:
It would be nice if people stopped talking about class A B and C networks. Such things haven't been used in a very long time and are worse than meaningless and are best used as "gotcha" questions on interviews or punchlines of jokes about greybeards.
By class A, do you mean a network with a /8 netmask or do you mean that the first octet is between 0 and 127? By class B do you mean a /16 or the first octet is between 128 and 192? Why are you talking about classful networks in the first place?
For private addresses, the distinction is silly. RFC1918 defines several networks that shouldn't be globally routed, including 10.0.0.0/8 (a true class A), 172.16.0.0/12 (in a class B network range but consisting of 16 contiguous "class B" networks), or 192.168.0.0/16 (which is 256 contiguous "class C" networks).
As Kazoom said, people talk about subnets based on their subnet mask, not the size of the first octet (which implied subnet mask in the "classful" days).
And, if you're asking this question because it is part of some coursework, you should get pissed at your instructor for not getting his head out of the early 1990s (1993, according to wikipedia). Your instructor is wasting your time and probably money as well, unless your class is "the history of the internet and antique routing protocols" which hopefully also would include uucp and bitnet as well as rip and decnet and maybe SNA.
Solution 3:
If a /24 is good enough for Linksys, Netgear, Buffalo, Apple, and every other consumer-grade device manufacturer then it's good enough for me.