According to page 144 of the PHB under Armor proficiency it states that
You cannot cast spells.
However the warcaster feat claims you have learned to perform Somatic components while wielding weapons or a shield in one or both hands.
Now, logic would dictate that shields wouldnt hinder Vocal Components, and you can hold a spell focus in the other hand, Why would one need to have proficiency in shields to cast, if they Have this feat?
I understand stand that RAW would dictate it is simply not possible, but I am unsure as to why.