What justifies the authority of a bank to create money when they make loans? This is somewhat of a political or philosophical question.

As explained by the Bank of England and elsewhere, the majority of broad money is created by credit to banks' accounts when they make loans. "Loans create deposits, not the other way around."

What is it that gives the banks the power to do this? In other words, why can't I do the same thing? With what I currently know, it seems unjustified.
In attempting to justify it, I'm wondering if maybe there is there some kind of cost to creating or debt created by these deposits and this somehow justifies their ability to create them. Do they owe something to a central bank or the state upon doing it?
This is due to Fractional Reserve System. In fractional reserve system when you make a deposit at a bank bank is required to keep a bit of it as a deposit and it is allowed to lend out the rest. 

So for example if Central Bank makes an initial money injection into economy. Let’s say 100€ (and it does not really matter whether it’s by helicopter drop or directly putting them in banks) the money will eventually be put into deposit account sooner or later. Once money is deposited with fractional reserve being let’s say 10% the bank keeps 10€ and lends the rest 90€. The 90€ again sooner or later gets deposited once the lender spends it so it will end up at some bank which will keep 9€ as reserves and lends rest 81€. In the end using this system private banks create from original 100€ a 1000€ worth of money supply (the final effect can be calculated using the multiplier ($1/ra)$ where $ra$ is the reserve ratio so with 10% reserves original 100€ creates 10 times as much money. Although as pointed out in the article its not inevitable the money supply will increase to its maximum possible value given multiplier as its not guarantee that households will put later money into deposit accounts or bank could just decide too keep full amount as reserve because it does not find profitable to lend money or there can be lending restriction imposed by regulation so the 1000 should be viewed as an upper limit on the maximum new money that can be created.

You could also do this. For example, if you convince your friends to give you deposits and then you keep only a fraction of those deposits and lend the money out to some other friends you will create new money (although if you are hell bent on doing this first check local laws in some countries maybe you can’t just do this without license). But in principle anyone could do this. In past, like during the Renaissance or even in more ancient times even many private money lenders did this.