せいにする => Blame... N2
Cause, reason
~むきがある(~向きがある)     => There is a tendency N1
させてあげる => (Allow) N4
Allow
てみせる => I'll show you ~ N4
Purpose, target
姿を見せる => figure; appearance N3
Ability
に...ができる => complete N4
Completed
できる => Can do something N5
ときているから/ときているので => because of ~ N1
させてくれる => Let me... N4
Allow
...が...を...みせる => make it look like... N4
Base, base
~あるまじき => ~ Unacceptable, not allowed N1
Ban
むきもある => There are people… N3
Of course