As far as I know, we don't really have an answer. Kruchev would go on to be removed from power two years later and placed under house arrest, where he died 7 years later.

He most likely knew things were out of hand at that point and a resolution was necessary. The removal of missiles from Turkey and Italy and a guarantee of Cuba's independence by the US was much more then what the US got out of it so who cares.

Since JFK needed to satisfy the, mostly angry, population he needed a win, Kruchev probably hoped that due to the much more closed political system he wouldn't need to do that, oh how naive he was. The party took this as a huge hit to their ego.