That is up to you to quit smoking
Again, that is up to you to know your man and find out what relaxes him
Are these sentences grammatically wrong?
I think "that" in each sentence should be changed to "it" to make the sentences grammatical.
It is up to you to quit smoking
Again, it is up to you to know your man and find out what relaxes him
But I have seen 1 and 2 sentences quite often used by native speakers.
Perhaps, is "to quit smoking" and "to know your man and find out what relaxes him" modifying "that" ?