I signed a transaction with a wallet that doesn't have sufficient balance, this is what I got: min relay fee not met.
That means your transaction did not reach the minimum fee for other nodes to relay your transaction (0 fee because of 0 funds).
It was possible to get zero-fee transaction relayed (and confirmed) in the early times of BTC. But this probably won't ever be the case again.
I'm trying to understand bitcoin why its not possible to create a transaction in the network with an empty balance..
Its not possible because you don't have any UTXO's (unspent transaction outputs). Read more here:
https://en.bitcoin.it/wiki/Transaction#Input.. and what are the network rules, how miners validate transaction then ?
You find the awnser in the first 2 chapter here:
https://en.bitcoin.it/wiki/Mining