why is it when I wash my car my dad has to wash his after... and then the week after also? like its a competition?

cause he cant think for himself and likes to copy you

Wash your car when it needs it and get on with your life. Don't worry about when your dad washes his car, unless he never washes it at all, which would be neglectful and a sign of bigger problems in his life. Until then, consider your own life to be pretty good right now if this is the biggest thing you have to concern you (some nutty, imaginary competition with your dad).

Does your Dad's car not get dirty just the same as yours?.
My son washes his car every week or so, I wash mine every year or so.
You either wash your car because it's dirty or because you like washing cars.

he sees how nice your car looks and wants his to look too

They get dirty and clean at the same time. Be glad your dad does not make you wash is car.

Why would you imagine that we would know why he does this better than YOU do, when he's YOUR father?