Why did the Boers resist British rule?

I would argue that the Boers resisted British rule on
nationalist grounds and on the grounds of what we would now call
self-determination.

The Boers were not British.  "Boer" is
the Dutch word for "farmer."  They were Dutch with some who were French or German.  They
came to what is now South Africa when the area of the Cape of Good Hope was controlled
by the Dutch East India Company.  The Boers generally felt loyalty to the Netherlands
and to Protestantism as opposed to England.  As England came to take control of the
area, the Boers resisted.  They did this because they felt that they were Dutch and that
they should not be ruled by English people.  In addition, they felt that they had been
there first (before any other whites, at least) and that that gave them the right to the
area.

So the Boers resisted the British largely because
they were Dutch and didn't want to be ruled by English people who were
Anglican.