I will try and minimize my personal opinion, but provide scripture (mostly) instead:
The ideal primary responsibility of the wife is to:
Titus 2:3-5
"3 Older women likewise are to be reverent in their behavior, not malicious gossips nor enslaved to much wine, teaching what is good, 4 so that they may encourage the young women to love their husbands, to love their children, 5 to be sensible, pure, workers at home, kind, being subject to their own husbands, so that the word of God will not be dishonored."
1 Timothy 5:14
"14 Therefore, I want younger widows to get married, bear children, keep house, and give the enemy no occasion for reproach;"
Proverbs 31:10-16 (etc.)
"10An excellent wife, who can find? For her worth is far above jewels.
11 The heart of her husband trusts in her, And he will have no lack of gain.
12 She does him good and not evil, All the days of her life.
13 She looks for wool and flax, And works with her hands in delight.
14 She is like merchant ships; She brings her food from afar.
15 She rises also while it is still night, And gives food to her household, And portions to her maidens.
16 She considers a field and buys it; From her earnings she plants a vineyard."
Considering those, if we return back to 1 Timothy 5, vs. 8 this time, it seems that the logical conclusion for the ideal primary responsibility of the man would be to:
"8 But if anyone does not provide for his own, and especially for those of his household, he has denied the faith and is worse than an unbeliever."
Especially as we reflect back to the garden of Eden and the curse:
Genesis 3:17-19
"17 Then to Adam He said, “Because you have listened to the voice of your wife, and have eaten from the tree about which I commanded you, saying, ‘You shall not eat from it’;
Cursed is the ground because of you;
In toil you will eat of it
All the days of your life.
18 “Both thorns and thistles it shall grow for you;
And you will eat the plants of the field;
19 By the sweat of your face
You will eat bread,"
^^These are not just "cultural" passages...these are either God's commandments or godly inspiration which applies today. There is no scripture explaining that such verses no longer apply in the 1st century.
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I do believe God's expectation, or the ideal scriptural positions to take would be that the man provides the majority of income, while the women uses that income to take care of the household and work well at home.
Now, like others have mentioned, maybe there are men who are truly unable to work, or at least provide sufficient income. Or maybe it just helps to have the women also provide financially. I do not see that as a problem, as long as she is still taking care of her primary role. Based on scripture, I don't think it's right for a man and a woman to swap roles just because they feel like it.
Understand that I agree that women and men are EQUAL. Equal, but different as far as the authority or responsibility that they have before God. In Christ, there "is no male nor female..." in terms of salvation--and in heaven we will just be spirits, no gender...but that doesn't mean that while we're still on Earth that we don't have to assume the gender roles clearly expressed by God.