What is the correct expression “it is up to you” vs “that is up to you”?

Question

1. That is up to you to quit smoking

2. 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.

3. It is up to you to quit smoking

4. 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" ?

Answer 1

Yes, I would change both sentences from "that" to "it." It's up to you has two definitions: the first that something is someone's decision, and the second that something is someone's responsibility.

It's up to you whether we get chicken or steak. (decision)

It's up to you to order the food. (responsibility)

If up to somebody is followed by an infinitive, it indicates responsibility.

That's up to you is usually used for decision, not responsibility. So in sentences with an infinitive structure after up to you (like both of your examples), I would expect it and not that.