Revealing mistake: When Chandler and Monica try to change the babies, Courteney Cox's pregnant belly is visible. (00:16:20)
Revealing mistake: When the first baby is born, Monica and Chandler are asked by the doctor if they would like to cut the umbilical cord. However, just before this line is delivered, the baby is moved and its navel is visible.
Answer: The statements that she's contradicting (that it is common, it happens to every guy, and it's not a big deal), are the things that a woman commonly says to a man who is suffering from erectile difficulty, typically to assuage his bruised ego. However, most men do not believe that these statements are true, as evidenced by Chandler's outburst. He's so caught up in the proof that women are lying about it that he gives himself away.
Rooster of Doom