I never understood double entry bookkeeping and that's where the author immediately loses me again: Early on after 4th diagram, author includes sentence : "Because every transaction appears twice, once positive and once negative" There is something so obvious about this to accounting folks that they always make the massive jump without any explanation. The previous diagram absolutely does not have positive and negati…
It's just a convention to be able to capture the flow of money. Roughly, money comes in via Income, stays in Asset, goes to Expense (there is also Liability and Equity). Let's consider a home, as an asset. You could have got it with your own money (`Asset:Bank -> Asset:House`), or by taking a loan (`Liability:Home Loan -> Asset:House`). Both have very different implications. If you are just tracking current value of home, it won't capture the whole picture. E.g. if you want to sell the house, the price is going to be different in both cases.
Double entry is just a way to track the flow of money from these different categories of account. Once you have that, you can do a lot over it, generate all kinds of report that companies can use to understand their operations (and to share with investors).
There are even attempts to go beyond with triple-entry account, etc. I think the way to look at it is, companies need a way to understand and report the flow of money, the current state etc. Double entry helps with that. And they way it helps, it to keep track of both where money came from and where it went.