Yes, studies have shown that a person fights with who he or she loves the most. This is because you are more likely to speak your mind without fear when you are around people you love; you are more likely to have a quarrel with them.
You also fight people you love the most because sometimes they do not live up to the expectation you have of them, you expect them to put your needs as their priority. Failure to do this often results to constant fighting.
Fighting allows you focus on your problems that need to be solved before they become too large, that why a healthy relationship cannot be built on silent treatment.