Apparently with the Vietnam War needed additional financial resources, President Johnson was looking for looking under the couch cushions for more money to spend. When it was brought to his attention by an article in the Washington Post that in 1967, 155 (I have seen figures as low as 115) household returns had no federal tax liability despite incomes over $200,000; all of this being done legally. Apparently included in this account were twenty millionaires and the rest were ordinary citizen. So obviously something needed to be done. These people were not past of the government, so they had to be dealt with.
These individuals had successfully used the existing tax loopholes available (like municipal bonds, donations, etc.) to legally evade paying taxes. The revelation attracted further media attention.
So the Nixon administration attempted to correct this transgression.