Why is copper(II) carbonate not selected as an unknown compound for back titration? (Whereas another unknown carbonate is used instead?) Why is copper(II) carbonate not selected as an unknown compound for back titration? (Whereas another carbonate is used instead)

I know that the carbonate to be provided on the day (not Copper (II) obviously) will be reacting with excess HCl. The excess HCl will then react with NaOH to determine the concentration of HCl and eventually Molar Mass of the provided carbonate substance. 
NOTE: phenolphthalein is the indicator being used
Copper is a transition metal. As such, its ion will be a Lewis acid. The effect will, as with iron, be stronger with increased charge--so Fe(III) salts of strong acids give acidic solutions, more so than Fe(II) salts of the same acids. 

This is because lone pairs can be donated into the empty d or hybrid orbitals from water. The structure produced in this way tends to lose hydrogen ions. This means that the acidity in your experiment has two sources for hydrogen ions.