Yes. Because that is a cultural view. There is enough evidence that different cultures handled housework in different ways, in which that work was delegated instead to the elder just to mention one on top of my head.
Something to be clear here: Having a misogynistic view on something doesn't make you automatically a bad person or be misogynous. This applies to most unintended microaggressions (Which happen often). Instead of feeling on the defensive, it's a chance to reflect on what sustains that aggression in oneself. And while the work is difficult, it's worth reviewing and growing from it.
I guess if I say: no, it's not a mysoginistic view, I'll put you on the defensive, so I'll just share a few scientific correlations and raise a few questions. You're free to reflect on them, or not, for this case in particular.
Let's take household out of the equation and look at something else: Women are more organized than men.
This is not my take on the matter, but rather conclusions that have been drawn from both psychoanalytical studies (mostly personal preferences) and executional studies based on multitasking, in which women perform slightly better than men, on average, when given sequential tasks. (there's also some interesting stuff about how performance in women varies with their menstrual cycle.)
What can we perceive as good household? Well, I guess you could list a number of things, but I don't think it's hard to imagine that being good in sequential tasking is a positive, if you're aiming for efficiency. The personal preference thing is a bit muddier, because it does raise the question: is that a trait derived from biology, or ingrained by cultural pressure? Better studies probably need to be designed to answer that one, but there's an established association.
So my statement was not mysoginistic, because I didn't base it on any perceived notion of what a women's role should be. I just based it on some evidence that women are, on average, better at something that's obviously important for good household, and probably more inclined to do it better, because they value an organized room more than men. If I was given a big sample size of people, complete strangers that I know nothing about, and I was asked to pick one to clean my house, I'd probably pick a women. Would that be me perpetuating stereotypes? Or would I be making a slightly more educated guess than closing my eyes and randomly picking someone? Should I pick a man just so I don't offend a women that might think I'm doing it out of some mysoginistic view? Where's the equality/honesty in that?
Now, you might say that these studies had flaws, or that some of the conclusions don't correlate to housekeeping in a robust way, and if I want to make that sort of association, I'd need better studies designed to correlate the two. I completely agree, no arguments there, but there's something there.
Going back to the original statement: Women are more prone to housework than men.
Assuming that you believe in what I said, is this still a mysoginistic phrase? Should I retract the statement because you're offended or micro-aggressed?
(you can check it out for yourself with a small amount of research, or you can check pubmed and probably find articles on this type of stuff quite easily)
Follow up question: does this mean, in any sort of way, that a women's role is to do chores?