Medical textbooks have descriptions of classical ways that conditions and diseases present. Wheezing, coughing, chest tightness, shortness of breath are all attributes of asthma, but not all people with asthma experience these symptoms or recognize them as such.
Feelings of fatigue or lack of energy are relatively common (although not everyone with fatigue has asthma).
Often, people will limit what they do to avoid feeling out of breath. They don't describe this as "limitation of daily activities due to bronchospasm or uncontrolled asthma". They say: "I don't like to exercise." If asked why, they may explain: "I'm just not good at it...I get out of breath; I must be out of shape." Now it's true that being "out of shape" can cause such feelings as can many other medical conditions, but careful discussion , validated questionnaires (such as the Asthma Control Test) and objective lung function testing can help pick up asthma that may not have been suspected.
Why is diagnosing asthma important if the person experiencing it hadn't noticed anything wrong? Because people with asthma can suffer from decreased quality of life and health whether or not the asthma is recognized. Moreover, with recognition and proper management, these same people can (mostly) achieve a good quality of life with few or no limitations in activity and decreased risk of serious asthma attacks.