The rationale behind keeping kosher is first and foremost the fact that the Torah says one must. In Judaism, even if someone were to offer that eating pork is unhealthy, that is still ultimately not the reason that they do not eat it. They do not eat it because God said they shouldn't. They believe that God restricted the food intake for reasons best known to Him.
It is impossible to know the original reason for keeping kosher according to the Torah, since the Torah does not give provide a comprehensive explanation. It explains that Jews should not eat blood because the life is contained in the blood, which explains part of shechita, kosher slaughter; and the Torah is also clear that they should not mistreat animals by causing them pain, which is also an element of shechita (althogh one would argue that perhaps it does cause unnecessary pain); but the only explanation given for the prohibition against eating certain kinds of animals, or for the separation of dairy and meat products is a simple assertion that doing so is holy.
And for Jews who observe this particular Jewish law, that is rationale enough.