We proved it's breakable. Do you want your security to depend on an oath with holes in it held by someone we don't know where is? I mean, it's not even that I don't trust the Headmaster but what if he's seriously injured by the backlash and just can't die?
Ultimately we'll have to undo the other oath ourselves if he can't undo it and can't explain to us what's going on. But a second oath is a stopgap measure and the terms would be slightly different and safer for us.