The reason is that any acquirer will ask for the consent of a very high threshold of shareholders for an acquisition. We're talking sometimes as high as 95% of shareholders. Note that this is not people with options, but those who are actual shareholders. In practice, this isn't a problem because usually you have the shareholders generally lined up before you start the process of sale. And you also have drag-along provisions in the various stock agreements where the stock holder agrees to vote with the majority of holders of that class of stock, so large holders can pretty much make a merger happen if they wish.
In this case, Jeremy can claim that he is owed a huge percentage of the equity. Because there are no written agreements where his rights to the equity lapse, regardless of how long he worked, that putative equity is his. And in that case, more than enough for him to veto the merger.
Tough spot for Kyle to be in, but I'm shocked with his prior startup experience that he didn't get this resolved earlier. It would have been easy to have something be written up and signed for next to nothing right as Jeremy left.
I sympathize with Sam and Kyle over this, but unfortunately the legal world is an alternative universe, and they need Jeremy to close the deal.