My mom tried to teach us ways to stay healthy, but I got cushing syndrome. Why is that?

Not your fault. Quoting dr. Loh:primary cushing's syndrome is the result of an endocrine active mass of adrenal gland cells that become so not as a result of lifestyle habits (good or bad). It's not your fault, but fortunately often completely curable. There are secondary cushing's syndromes related to medications doctors give to treat certain conditions, and it becomes a balance of benefits vs. Risks.
Not lifestyle caused. Cushing's syndrome is caused by a tumor producing extra hormones causing elevation in a stress hormone (cortisol) or by overusing steroid pills (probably for inflammatory diseases: rheumatoid, asthma...). It's not lifestyle related. You could live, eat, make perfectly healthy lifetyle choices and still could get cushing's syndrome.
Nothing you did! Cushing's syndrome, which is caused by an overactive adrenal gland (or both glands) is an "auto-immune" disorder, which can happen to anyone, regardless of their diet or habits. [it can also be caused by taking some form of cortisone in pill form, which I am assuming is not your situation.].