why type 2 FIR cannot be used to design high pass filter
Type 2 filters are even and symmetric.  A signal with a frequency of $f_s/2$ is just a scaled version of [+1,-1,+1,-1,+1,...].

That means, at $f_s/2$, the response of a type 2 filter will always be zero as the coefficients of the same magnitude are an even number of samples apart so they cancel each other out.

A filter with a magnitude frequency response of zero at $f_s/2$ makes a very poor high pass filter.