First, Cobb silences her entirely justified objections by shout-screaming "There's no time for this!" Maybe you could justify this if, in fact, they were in a position where they had no way of succeeding unless Cobb knew. But then he doesn't even use that information. He immediately has her tell it to the other members of the team so they can do all that air-duct-scuttling bullshit while he watches through binoculars.
Predictably, Mal appears and shoots one of Cobb's team members, effectively ruining the mission (or at least making it a lot more difficult and confusing). Had Cobb not insisted that Ariadne tell him about the secret way into the base, Mal would never have shown up (because Mal is Cobb's evil subconscious, so she only knows what he knows). There wasn't even any reason to tell him about it, either -- Cobb could've just asked, "Hey, is there another way into the base? There is? Good, tell them about it while I plug my ears and sing 'Black Hole Sun' to myself for a minute."
"Black Hole Sun, dreams are dumb, dreams are duuuuuumb ..."
His "There's no time for this!" outburst is especially ridiculous because he's asking Ariadne to take an extra step explaining everything to him, making the whole thing take longer. She could've just relayed the information directly to the rest of the team in less time than it took to unnecessarily involve Cobb, and they would've avoided the "murderous wife ghost" factor in the process.