Airplanes can be purchased as CERTIFIED from aircraft manufacturers. You can also buy KITS/HOMEBUILTS and assemble them yourself. PLANS are available that show the builder how to manufacture his own materials. And, there are the people who actually DESIGN an airplane, then BUILD their own parts, and ASSEMBLE a truly D.I.Y airplane.
It seems like a monumental undertaking, but actually, it’s not all that uncommon. Here is a story that shows one particular young fellow who did it. Not once, but many times!