I cannot remember if it was Rashid or Mother Summer who explained to Harry about the Gates, their purpose, and who are guarding them at the moment. What I remember is it is all about balance. At the moment it is the Winter Court who mainly guards the Gates and battles would be intruders. This makes them very strong and dangerous if Mab or Mother Winter abused that power. Thus it is the Summer Court's duty to keep the Winter Court from going beyond their resume description for keeping the Gates safe. So they may seem at odds, but in truth they are really not, as we saw in Battle Ground, they can and do cooperate against a common enemy. That is why Aurora had to go, infected as she undoubtedly was, her aim to create an unbalance, triggering a war between the Courts and leaving the Gates vulnerable to the Enemy.