My dad's MRI showed abdominal aorta aneurysm. Our doctor says to come back after three months. Why should we wait?

Depends on size. Not every AAA needs to be to be treated immediately with surgery. As the aneurysm grows the risk of rupture grows. Surgery, though, is very, very major and has to be worth the risk. Endovascular stents may lessen the risk. Your physician and/or a vascular surgeon will advise based on his health status, research data and aneurysm type. Blood pressure control and smoking cessation are vital.
Changing size. People often get studies which show them problems they weren't expecting. If your dad was incidentally diagnosed with an aortic aneurysm, the doctor may want to repeat it in a few months to make sure it isn't increasing in size. If it was a large aneurysm, he would likely recommend getting it fixed since larger aneurysms are more likely to rupture.