It's important to note that Nixon hated just about everyone. He felt Jews were born spies. His drug laws were created because he saw Black people smoking weed on TV. As to India, Indira Ganghi seemed to be one of those people who just didn't feel the need to really bend the knee to Nixon. To be impartial about the matter, it does seem like she didn't really have a high opinion about the man either. When Nixon was on his road back to power in 1967, he apparently had a meeting with her. She seemed bored and frankly disinterested in what he was saying. She asked an aide in Hindi how much longer this meeting would take. Nixon got the general hint even though he didn't know what she was saying.^1 When he became president, he had a much warmer relationship with the Pakistani leader, Yahya Khan. This became a more relevant issue to Gandhi as India and Pakistan were headed towards war. Gandhi was carrying on the policy of nonalignment. She didn't want India falling into either the US or Soviet Union's sphere of influence. Despite this, Nixon noticed that India was becoming uncomfortably close to the Soviet Union.
As I mentioned earlier, India and Pakistan were inching towards war. The President was getting intelligence briefings that India was gearing up for war. About a month before India went to war, Gandhi was in Washington where Nixon pressed his case for no war. He wanted Pakistan intact, and Khan to remain in power. You see, Nixon was using his warm relations with Khan help him open a channel with China and get China out of a two decade long diplomatic freeze. To really help drive home the point, Nixon essentially told Gandhi that the great powers would take decisive action against India if they felt that Pakistan would lose its eastern half of the country. Gandhi apparently gave Nixon enough assurances that he felt India wouldn't go to war. A month later when India declared war, Nixon was furious. He felt he had been duped.^2
Now remember when I said Nixon felt that India was getting uncomfortably close to the Soviet Union? What Nixon (and Kissinger) didn't know was just how close they had become. Gandhi left her meeting with Nixon assured that India can't launch a war against an enemy that literally surrounds them. Pakistan was a potential existential threat, and the US told them it didn't matter. Nixon wanted a mortal foe to remain in one piece and continuing to surround India. She talked to Brezhnev who assured her that he would support India's war effort.^3 India went to war, and pretty much wiped the floor with Pakistan. When it became clear that India was on the verge of total victory, Nixon ordered the USS Nimitz into the Bay of Bengal as a warning to India. It was his hope that this would scare India enough to pull back and not take all of East Pakistan. India notified the USSR about this turn of events and asked if they still had their support. The USSR assured them that they did, and responded by sending nuclear armed submarines to the region.^4
For Nixon, India went from a potential ally, to a regional power unofficially allied to the USSR. In his head, this was all Gandhi's doing. She had showed him little respect, lied to his face, destroyed a politician he was friendly with, and outplayed him with the use of Soviet military aide. What's more, in the western press, Gandhi was hailed as a hero. She had liberated the oppressed Bangladeshis, and could have pushed the war further to potentially take back lost territory in Kashmir; maybe even pushed into Western Pakistan as well, but didn't. For Nixon, a man who hated everyone, and trusted no one, this essentially solidified his utter hatred of Gandhi.
^1 "The Blood Telegram: India's Secret War in East Pakistan."
^2 "Nixon, Indira and India - Politics and Beyond"
^3 "For the President's Eyes Only: Secret Intelligence and the American Presidency from Washington to Bush"
^4 "Body of Secrets: Anatomy of the Ultra-Secret National Security Agency"