There are two possibilities.
- New hires don't really have anything to tell their employers, but there is a lot they need to know: what should they bring on the first day, what are the working hours, what should they wear etc. He has grown tired of waiting to be asked these things with long complicated preambles so he has developed the habit of just telling new hires all the information. When a question starts he assumes it's one of the standard ones he's heard thousands of times before and he can't be bothered to listen to you explaining why it's important to know what time you start or whatever, so he just blasts all the answers at you.
- He actively doesn't want you to change or negotiate anything, and his conversational technique enforces this.
I think the first situation is more likely. In this case all you need to do is get through to him that you have an unusual situation. Call (be sneaky and call after hours to leave a voice mail if you like), email, or stop by, and say "My apologies but I have a family emergency that may delay my start date. Will the 15th be ok?" You don't need a whole pile of "points" to "convince him" - either they will be ok with a delayed date for this reason or they will not, it's a short conversation. By the way you should decide in your heart before the conversation: if they say no, will you decline the job in order to deal with the family situation? Decide in advance so that if they say no you can immediately free them to find a replacement for you.
If you are in the second situation it may be harder to reach this person or to ask him anything. In that case it is even more important to get to the point right away. Do not summarize to him when you were supposed to start, do not tell him the details of the emergency or why this person is important to you or why you are the only one who can deal with it. Just say "I need to change my start date to the 15th to handle a family emergency. Is that ok?" The quicker you get your question out the better chance you will finish it before he interrupts and takes over.
As a general habit I find it serves me well, when talking to superiors, to lead with the headline, not the background. "I need two weeks off starting now." Pause. "I have to [whatever.]" Pause. Then wait to be asked for details. This is more efficient than paragraphs of background before the request. An irritated boss may say no to a reasonable request. A calm boss may save you a ton of time may just say yes right away, or will ask for the information they need. And when asked for information, again provide the most important part first.