Potentially OP could do it. But from the wording of the comment, it sounds like OP is the main earner in the household, so if they have a spouse then the net income opportunity cost from not working would be lower for the spouse.
As to why it's cheaper, that's a calculation they have to make. If the spouse's net income (looking at marginal tax rates) is greater than 3k a month, then it's not cheaper.
And why do you think having a full-time tutor is cheaper than group care at a school?