nomenclature of citric acid
The "-oic" ending means to convert the carbon into a COOH group, not that there's an additional COOH group added to that carbon.

Look at your main chain. You have five carbons, of which carbons 1 and 5 are fully oxidized, hence "pentane-1,5-dioic acid". If the "COOH" group was counted as an independent entity adding an additional carbon, then it would be a three carbon chain, to which was added two COOH groups.

That's why it can't be a 3-oic acid - that would imply that the third carbon of main chain has been oxidized to a COOH group (which is preposterous), not that there's a COOH group that's been added. Instead, the COOH group (carboxy) has been appended to the three position, and the molecule is named accordingly.