This is very dependent on what one defines as a disease. There are people who only count acute conditions and/or infections as "diseases" though I wouldn't have expected a doctor to make this distinction. Under this definition, asthma would not be a disease, but a "chronic condition", for example.
I found an interesting article What is a disease which while mostly applicable to your question about asthma discusses the classification of osteoporosis
One example is osteoporosis, which after being officially recognized as a disease by the WHO in 1994 switched from being an unavoidable part of normal ageing to a pathology
So that used to be not counted as a disease to being called one. I recommend asking your doctor about it if you are curious about their reasoning - it might just be that they meant it isn't an infectious disease. If, however, they think asthma is really not a disease that needs to be managed, consider switching doctors - untreated asthma can lead to serious problems.