How come i have bronchial asthma, but nobody else in the family has it?

Many causes of asthm: Asthma certainly has genetic factors but there are many other factors that may be involved in developing asthma. These include allergies, infections, the environment, personal habits (e.g. Smoking), and many others.

Roll genetic dice: There are multiple genes involved in the bronchospasm control mediators involved in asthma. Your siblings obviously have different genes as did your parents & all may have bits of the genetic info but not enough to be symptomatic. They may have milder forms like cough varient asthma, that are often unrecognised. 3 of 4 in my family had forms of it, 1 had no symptoms ever.

Not genetic...: Asthma is not a genetic disorder, per se, so it entirely possible for you to be the only family member who has it. Asthma can be allergic or intrinsically induced (for example post-infection). Although there is no cure, there are many treatments available to keep you as free of symptoms as possible.

Bronchial asthma: You can have bronchial asthma without having a family history of it.