As a new parent... diapers. Disposable diapers in particular.
Imagine being told as an engineer, you need to design a device to contain the vilest, grossest materials known to man. Both liquids and goopy solids. This device must have 3 tight seals against a constantly moving and wiggling life form of inconsistent size. Said life form has notoriously delicate skin, so the materials you can use are drastically limited. It must be able to be removed and installed in seconds by amateurs running on approximately 14 minutes of sleep...
... and it has to cost about 30 cents a unit.