That reaction is correct in terms of electron book keeping, but in reality most carboxylic acids can't be converted directly to anhydrides like that. The -COOH that adds is a much better leaving group than the hydroxide that gets booted out, so the reaction is very uphill in that respect. One way to get around this is to convert the acid to an acyl chloride with SOCl2, and then add carboxylic acid. The second step can be either acid or base catalyzed.
As to why the carbonyl carbon doesn't act as the nucleophile in the second step of anhydride formation, my best guess would by that the resulting product is less stable thermodynamically. I tried drawing out a mechanism with CH3COCl plus acetic acid, and came up with a central carbon bonded to -OH, -COOCH3, -CH3 and -Cl.
Another possibility is that under acidic conditions most or all of the carbonyl carbon is protonated, so it can't act as a nucleophile. And under basic conditions this is all a moot point because the deprotonated carboxylic acid has 2 equivalent nucleophilic oxygens.
As a side note, anhydrides can be made directly from DI-carboxylic acids in a cyclyzation reaction the involves a loss of water. This requires a high temperature, because the reaction is favorable only entropically.