When you make a change in Git (and Mercurial) you're essentially making the following statement:
This is the way things are now. Forget whatever happened in the past, this is what matters.
Which is subtly and importantly different from what a lot of people assume it should be:
Add this patch to the corpus of all changes which have ever been made, and are what defines the most recent version.
The example linked above has a lot of extraneous confusing stuff in it. Here's an example which cuts through all the crap:
A / \ B B | A
In this example, one person changed a files contents from A to B, then back to A, while someone else changed A to B and left it that way. The question is: What to do when the two heads are merged together? The answer deeply depends on the assumed semantics of what the person meant when they reverted back to A. Either they meant 'oops I shouldn't have committed this code to this branch' or they meant 'this was a bad change, delete it forever'. In practice people mean the former the vast majority of the time, and its later effects are much more intuitive and predictable. In fact it's generally a good idea to make the separate branch with the change to B at the same time as the reversion to A is done, so further development can be done on that branch before being merged back in later. So the preferred answer is that it should clean merge to B, the way 3 way merge does it.
Unfortunately, this decision comes at significant cost. The biggest problem is that it inherently gives up on implicit cherry-picking. I came up with some magic merge code which allowed you to cut and paste small sections of code between branches, and the underlying version control system would simply figure out what you were up to and make it all work, but nobody seemed much interested in that functionality, and it unambiguously forced the merge result in this case to be A.
A smaller problem, but one which seems to perturb people more, is that there are some massively busted edge cases. The worst one is this:
A / \ B B | | A A
Obviously in this case both sides should clean merge to A, but what if people merge like this?
A / \ B B |\ /| A X A |/ \|
(The 'X' here isn't a point in history. It's ascii art of two lines crossing over each other.)
Because of the cases we just went over, they should clean merge to B. What if they are then merged with each other? Since both sides are the same, there's only one thing they can merge to: B
A / \ B B |\ /| A X A |/ \| B B \ / B
Hey, where'd the A go? Everybody reverted their changes from B back to A, and then via the dark magic of merging the B came back out of the ether, and no amount of further merging will get rid of it again!
The solution to this problem in practice is Don't Do That. Having multiple branches which are constantly pulling in each others's changes at a slight lag is bad development practice anyway, so people treat their version control system nicely and cross their fingers that the semantic tradeoff they made doesn't ever cause problems.
