a lot of conservative organizations will frame [that graph] in such a way that they say "See, look how the inequality increases during Obama years.

Thats because
A) Republicans -- literally a Raegan cabinet member -- made the graph and selected the data represented in it.
B) The Raegan advisor who made the graph dont want you to see pre Raegan Era. Thats why their graph starts at 1973 and everyone elses starts before that. More data = bad!
C) Repubs blame everything on Democrats.