In the argument,

After we arrive at the result that

but also state that

it is concluded that H does not shatter the given d+2 points. (I understood this).

However you then stated:

"You cannot shatter your set for any set you choose. Therefore you cannot shatter any set of d+2 points"

How did we go from not shattering a given set of d+2 points to not being to shatter any set of d+2 points?