Weight vs aerobic: can I do both?

Personal trainer Matt Hart replies: You know what they say: 'Jack of all trades, master of none'. Well, in this case it's certainly true. You haven't been fed misinformation; aerobic training will work against your muscle growth, especially if you really want to develop your CV fitness.
Muscle growth stems from anabolic processes which are 'body-building'. This means you have to work hard with weights to break down the meaty fast-twitch muscle fibres and eat a calorie-rich diet to provide the energy and raw materials to build them bigger and stronger.
Aerobic work interferes with this process by competing for these calories and using them for fuel. If the aerobic work is particularly prolonged and strenuous, the body will even metabolise the muscle bulk for energy, whittling you back down to slenderness. If you work hard at both the weights and aerobic work, you'll look lean, toned and athletic, which you may consider a satisfactory compromise and, while I would favour this healthy balance, you may have other goals in mind.