Yep this attitude annoys me too, but it really really gets my DH riled up.
He hates the assumption that he wouldn't be as much of a parent as me, that he wouldn't be as capable, committed, or responsible for caring for our son as me just because he's the man.

We both work part time, at the moment my DH makes more about 2/3 of our income but up until a few months ago it was even and next year I'll probably be making more than him.
If someone needs to stay home with our sick child we work it out based on what we have going on and how close we are to where our son is at the time.

In some ways it's hard to be juggling all the time, but it's also really rewarding. We both get the careers we want and we both get to be active parents. Neither of us would want to miss out on either of those.