Lend me your brains

Why would I need two specific ratios, my brain tells me that any two ratios would work.

Imagine the set up in your head with two very differing ratios, and imagine this to be correct and working - now mentally grow one of the chain rings by a substantial amount.

My imagination also forces me to also lengthen the chain to accommodate the larger chain ring.

If i remember correctly, the distance your axle moves in the dropouts when you (say) add 1 tooth to your chainring is not the same as the length of 1 link of the chain.

At the very least it would involve using halflinks, although at £2.50 each these would be the cheapest part of the whole project.