The part that I understand in the intellectual sense, because I know or at least used to know how it follows from the math, but which just doesn't feel like it should be the case, is the whole "relativity of simultaneity" aspect of it. That there isn't an objectively true order in which events happen in, if the events in question aren't linked by cause and effect. That is to say, it is possible for one person to see an event A happen before another event B, a second person to see the two happen at exactly the same time, and a third to see event B happen first and then event A, and for all three of them to be equally right. It just feels like, on some level, there ought to be one objectively true order to time, a single valid timeline that all events can be placed in relative to eachother, and for time not to work that way feels so absurd as to not even be able to articulate why the idea feels wrong.