Everybody talks about LIBOR, and you don’t really hear much about LIBID. In fact, the BBA only fixes LIBOR and LIBID is left to free float if you like.
The fact is that most banks will need to borrow more than they will need to lend. Or rather, for each investment opportunity they see they will need to fund the investment by borrowing.
LIBOR is the rate at which banks believe they could borrow cash in the inter-bank market from others that want to lend it.
Movements in LIBOR reflect the existence or not of other sources of borrowing: why would you borrow cash from a bank at LIBOR when you can borrow from the central bank at a better rate?
And by the way, the reason that it is an offer rate is simply that the bank that lends is selling an asset: cash. The same convention applies when we talk about swap rates: buying the swap can be interpreted as buying the cash and paying a fixed rate of interest for the borrowing. Did you see that other article I wrote on these conventions?