Actually, the expression more money supply is not clarifying at all (i) which effect is desired abdand (ii) what really occurs, whence your (really natural) question.
What is implicit behind this expression is that commercial banks will have an easier access to (re-)financing. If commercial banks play their role of Money multiplier -- which is not that obvious since they may prefer to clean their balance sheets --, they will basically be more prompt to grant credits. Put differently and using an abusive but pedagogical term: they will be psychologically more prompt to waste money, and thus to stimulate demands here and there.
Since growth is very often conceived as being demand led, more demands (of goods or whatever) at a constant level of supply (of those goods or whatever) in turn means inflation, until levels of supply, here and there, adjust and create jobs, generate dividends, etc...
To conclude and summarize
Basic Reason of Why the Money Supply Needs to Increase?
Because one needs commercial banks to be more relax and play their role.
what would be wrong with keeping it the same as the economy grows [...]
The economy cannot really grows without leverage.
[...] or contracts
Bubbles may form and explode sooner or later in this case, which is nothing desirable.
Adjusting the money supply is a difficult balancing exercise for central banks.