Pink and red

I was always taught that pink and red clash, and should therefore never be worn together. I never understood this. I mean, given that pink is only red plus white, why does pink clash with red? And what's wrong with clashing colours anyway? My aunt loves pink and red, and manages to wear them together with great style. We thought we'd have a try too...
 

Red on a bright pink background. Little circles. A bit too bright but with a subtle pattern.

Red on a pale pink background. Big circles. Bold. 

Pink, red and a bit of green on a cream background. Checks. Clashes.