Why is adenine aromatic?
The $4n+2$ rule applies only for a conjugated ring.  If you assume that the amino group contributes a pair of pendant  $\pi$ electrons into the ring system then perforce you do not have a conjugated ring.  And even if you don't assume such a delocalization from the amino group, the cross-link within the ring system is still a stretch for the $4n+2$ rule.