Nobody says ' the training of Tuesday', yet they say this is correct over 'the training for Tuesday'. Any native English speakers on staff?
The training for Tuesday would mean that you are planning to do something on Tuesday for which you undertake (beforehand) a very hard training sesssion so as to be prepared for the event. The training of Tuesday sounds weird, unless you have a dog named Tuesday. Tuesday's training is both English and makes some sort of sense (not always an important criterion for Duolingo, I know...:)