"what makes me do something are A and B"
It is an awkward way to speak! The above is sort of correct, though. But it actually should be "make."
Instead, you should write:
The factors that make me do volunteer work are A and B...
The word factors is better than the word what.
With the dogs and cats example, just remember that you use the word "are" if it is plural:
what make me do something are your dogs and your cats
what make me do something are happiness and goodness
The concepts that make me do something are happiness and goodness.
The concepts that make me regret my crime are moral values.
What makes me lie is sneakiness.
The mechanisms that make me lie are illusions.
It is bad to start that kind of sentence with the word what.