Accountants use jargon in the same way that programmers do - to succinctly express commonly known and understood concepts. They do not use 'hard words'; if the words are 'hard' it's because the reader lacks the domain knowledge that accountants have been trained in.
The fact is that double-entry bookkeeping does not use negative numbers. Where confusion might arise is in the meaning of 'debit' and 'credit'.
'Debit' only means 'the left hand side', and 'credit' only means 'the right hand side'.
A debit is not a subtraction operation, nor is a credit addition. I suspect this mis-conception mostly arises because that's how it looks when a Bank 'credits' your account with your deposit - in fact it's increasing its liabilities (it owes you the money) which is recorded as an entry in the right-hand side of the liability column.
'Debit' only means 'the left hand side', and 'credit' only means 'the right hand side'.
Not only, and not even! The terms debit and credit have meaning independent of their columnar position on a traditional ledger. I could create a ledger with the columns reverse or (shocking!) use a computer program with a data structure that doesn't encode the concept of left or right.
I think about it like this:
CR / Credit / Creditors -> what the business owes
DR / Debit / Debtors -> what the business owns
> 'Debit' only means 'the left hand side', and 'credit' only means 'the right hand side'.
Well, it is a bit more than that. It is the two sides which must balance, so you put them on those sides in order to make them balance. For example, you would put assets and expenses on the debit side, liabilities and revenue and capital are on the credit side, so they will be added up because e.g. you would earn money (a asset) in the debit side and the equal number of revenue on the credit side, so you can see that they are equal.
Of course you could consider them addition and subtraction (in either order; the diagrams in the article use the convention that debit is positive and credit is negative, while you seem to be using the opposite convension) and then consider that they add up to zero, which is mathematically equivalent to the description above.
The diagrams in the article is another way; the arrows are pointing toward the debit side in these diagrams (so the Sales and Capital are shown as negative because they are in the credit side). ("Now, by convention, accountants flip the sign on all of the blue and pink nodes’ balances" is also because they are in the credit side.)
Or the "matrix accounting" that I had made up, where the balance is represented by the equation (which doesn't have any reference of "debits" and "credits", etc):
<BAL|FSV> = 0
(<BAL| is assumed to be a constant, while |FSV> is considered to vary over time and represents the financial state vector. (It is a kind of projective space.))
The fact is that double-entry bookkeeping does not use negative numbers. Where confusion might arise is in the meaning of 'debit' and 'credit'.
'Debit' only means 'the left hand side', and 'credit' only means 'the right hand side'.
A debit is not a subtraction operation, nor is a credit addition. I suspect this mis-conception mostly arises because that's how it looks when a Bank 'credits' your account with your deposit - in fact it's increasing its liabilities (it owes you the money) which is recorded as an entry in the right-hand side of the liability column.
edit: typo