Flyers: head up vs head down

I am swimming with a new coach and she is quite adamant that my breathe every stroke rhythm is holding me back and I *might* hyperventilate. I look at breathing as a choice. I don't breathe every time my head comes up, but rather do it for rhythm. As in head down strokes tend to lead to my hips dropping later in a race. So, I find the head up every stroke helps me with that. Is there any other reason why I *need* to take a head down stroke that she isn't explaining to me? I'm almost getting to the point where I'm tuning her out unfortunately, but if it's simply a 'hyperventilate' mantra it makes zero sense b/c bringing ones head up doesn't necessitate a breath. Is the only reason to take a head down stroke to avoid hyperventilating? I have asked her this question and received 'yes', but would like to hear from the forum brain trust on this. Thank you! If this is a technique issue by lowering the head that will make me faster I'm all for it, but I want to hear the how and why b/f I potentially disrupt the rhythm of my stroke.