Actually, the expression *more money supply* is not clarifying at all which effect is desired, 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](https://en.wikipedia.org/wiki/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 demands driven, 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](https://en.wikipedia.org/wiki/Leverage_(finance)).

> [...] or contracts

[Bubbles](https://en.wikipedia.org/wiki/Economic_bubble) 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.