[Grammar] Talking about the future

[Julie17]

In a coursebook I found an exercise about the different forms of the future. Students have to find the suitable form(s) for words in brackets.
The model answer goes like this:
... A: I'm attending /am going to attend a seminar on Wednesday, but I'm not doing anything on Thursday.
B: Thursday lunchtime would be OK, but I'll have to leave for the airport at 2 p.m.

I find it hard to explain why you have to choose 'will' in the last sentence. It's a plan, so the continuous form or going to should also be possible. Is it because of the verb 'have' expressing an obligation here:?:

 

[GoesStation]

I think the distinction the course book is trying to illustrate is so subtle that few learners would ever grasp it. I'm going to have to leave would be natural, too, adding a little note of subdued apology. This version is probably less likely than the one the author prefers.

 

[Julie17]

Unfortunately the distinction is too subtle for me, too. ;-) I would have used the form given in the book, but I can't explain why. Any ideas?

 

[jutfrank]

It certainly is difficult to explain. The best I can do is to suggest that will gives the sense of there being an inevitability of something happening, i.e., the speaker's having to leave by 2 p.m. (due to a prior obligation). This serves as a warning of a possible problem associated with the arrangement.

The speaker wants to say that there is a condition attached to meeting at lunchtime on Thursday. I believe the same principle is at play when we frequently use will in first conditionals to predict a possible real outcome of a condition. We could expand the entire thought to make its conditional nature clearer:

If we meet at lunchtime on Thursday, then I will possibly leave before we finish doing everything that we need to do during the meeting due to a prior obligation.

The speaker is predicting a possible problematic outcome.