Sea Demon, the problems with asthma is twofold:
1. Having an asthmatic attack underwater.
This can easily happen because of cold water, exercise and inhaling saltwater mist (from the regulator). Having an attack underwater is bad - can't sit and rest, can't take inhaler, can't take a decent breath from a SCUBA regulator. Bad news. But there is a more important reason for not diving with Asthma:
2. Pulmonary Barotrauma.
Even when not having an attack, some small airways in asthmatics remain blocked. During ascent, air in the blocked airways will expand (due to Boyle's Law) and.. pop! Gas bubbles from the ruptured airway then enters the lung's blood vessels, travels to the brain and blocks the blood flow there. Diver falls unconscious, gets paralysed and all sorts of bad, bad things. Doctors call this "cerebral arterial gas embolism". In english: bubbles in the brain's blood vessels. Bad, bad, bad. Keeps diving doctors and nurses up all night when this happens. (For the not-so-fun reasons, that is).
And there is another problem: What can be considered as
having Asthma? Mild wheeze once a week that goes off without treatment? Attacks that stopped for good when you reached puberty? The odd once-a-year severe attack that comes with a cold?
Most doctors do agree on one thing - if you have a history or past history of Asthma - go see a diving doctor before you suck on that regulator. In most cases, they'll do what divedoc has suggested.