I can see both sides, so there's no reason to argue about it. Also, my only sibling died from cancer at only 39 years old, so I'd give anything to be fighting with him about how to handle my parents aging, vs. going it alone...
Perhaps your brother is annoyed that your parents have done nothing in all this time (not packing per se, but purging stuff or passing it on to other family members so there was less to pack now when it's needed), or maybe he just doesn't like feeling that he HAS to deal with everything, since he's the only one who lives close. Whatever it is, acknowledge his feelings and work out a solution, or just move on without his help. No hard feelings.
I agree it's hard to imagine packing over 30 years of belongings in one week, but that's what movers are for. Hire a crew to pack their belongings for them and it will be done in ONE DAY. Seriously, I've moved several times and I'll never pack myself again. You can add packing and un-packing to the cost of a move for less than $600 (this includes the boxes, all sized to fit a moving truck), or hire out a crew to just pack your parents stuff and have your brother move them for even less. These crews that pack your goods do an amazing job too. They're liable for anything that breaks so they're more careful with your stuff than you can imagine.
My last thought is this, just because they take possession doesn't mean they have to move in this weekend. You could help them pack everything next week, hire a crew to pack up the moving truck and unload on the other end. Or hire the packers to pack everything, take your brother's offer of help to pack the truck and then you can help them unpack and purge next week when you arrive.
Take your brother out of the equation if you want to, just don't hold a grudge if this is what you decide to do. It won't help anything... If he tries to pick a fight about when/how/why, just say you've worked it out with mom and dad, and there are no hard feelings. Let him know what you're doing and if he's able to help in your timetable, that's great, you'd welcome some help.
Good luck!