For starters, the 70 million figure comes from the Black Book of Communism, a famously debunked work of propaganda that included Nazis killed in wartime as "victims of communism," and whose contributors were caught making up numbers in order to get to 100 million. Of the actual peacetime deaths under Mao, the majority occurred during famine which primarily originated from weather disaster, and was made worse through mismanagement. Even with these deaths, life expectancy from birth doubled under Mao:

Not only that, but Mao was instrumental in leading the Red Army to victory against Japanese imperialism, against the nationalist Kuomintang, and constructing the basis of socialism in China. Foot binding was banned by Mao. Industrialization dramatically increased under Mao. Land reform totally eliminated the feudal landlord class. Without Mao's contributions to solidifying socialism, there would be no successful modern China today.
With that context, it's easy to understand why China would take offense to a foreigner making light of one of their heroes.