I don't think it matters if you are a SAHM, a WOHM, or one of the tiny few who work part-time and share everything 50/50 with your partner.
To my mind, the question is what needs changing in the organisation of society to encourage greater equality? Or perhaps it would be more sensible to first look at what is preventing greater equality.
Part of that is questioning the SAHM/WOHM dichotomy. Does it actually need to exist at all? Isn't it an effective tool of the patriarchy to pit women (or their choices) against one another? Isn't that what the OP is asking? WHY is it not possible for many more women to find the middle ground. SAHPing has traditionally been a position occupied by the privileged few and that less than 10% of people (let alone women who are even fewer in number) achieve high-flying career status. Most women (indeed people generally) have lives that are extraordinary in their personal meaning and they simply work. It serves no purpose to argue the SAHM/WOHM continuously because this ignores the reality for the vast majority.
It is interesting that the SAHM/WOHM debate is so persistent in the face of this. What more proof do we need that structural sexism is alive and well and continuing to pit women against each other instead of spending their energy more constructively trying to find solutions to the work/home balance that are gender neutral.
How does this happen? Some women genuinely believe one way is better than the other. That's fair enough but only the unintelligent would assume that works for them will work for every single woman out there. No two families are the same. Polarised articles in the press also encourage it.
Cost of childcare also has an effect. The effect of our most-expensive-in-the-world childcare solution is that it allows only the poorest (through subsidy) or the well-off to take advantage of it (even this is changing as subsidy is cut). Leaving out the huge number of women in the middle. This results in many women having to choose the most economic solution rather than making a genuine choice, and it is often those forced into positions who, in seeking to justify to themselves their non-existent choice, become accidental propagandists, and because it touches a nerve with other women in the same position so it continues.
Capitalism is possibly the biggest factor. The pursuit of money is considered the most important point in the world. It's justified with arguments that claim happiness and equality can only be achieved if there is the money to fund these lofty ideals. As long as this idea goes unchallenged, there will always be inequality. It will always be the case that the high earner will be considered more worthy than the carer. Despite the huge amount of money saved by care of the eldery/disabled/children/mentally ill, because these activities do not generate money, they are considered worthless. I think that's an attitude we should be challenging strongly. If all the caring stopped and the government was forced to deal with it, the cost would be incalculable. That by itself should point to the value of caring and why it is important to enshrine this value in our society.
And why do we need money to fund childcare? Before industrialisation, women (apart from the upper middle and land-owning classes) coped without any formal childcare because they either took their children with them to work or could rely on an informal support network of extended family and community. Now no one wants to return to the past and taking your child to work with you isn't ideal in many cases, but it illustrates how capitalism works against the natural structure of society and removes the support networks that help women and protect children. It breaks down families and fractures communities. For what? A new ipad in every home?
We don't have to advocate communism but we do need to accept that capitalism left to reign unchecked is ugly and damages all but those at the very top. The most successful societies are those where equality is greatest and capitalism has had the brakes applied to protect the vulnerable (in which women always dominate the numbers) and to encourage community growth - which relies fundamentally on people not working all hours. People working 60-hour weeks cannot paint the local community centre, deliver meals on wheels, help out a struggling mum or babysit their grandchildren to allow the parents to work.
Capitalism needs to put a quantifiable value on caring. And even if it isn't actually paid to the carers in reality, it should be factored into the economic equations. Only then will be it recognised how important it is, and only with that recognition will there follow a improvement in status. This would result in more male SAHPs and also more families where more effort is made to split work/caring 50/50. And since capitalism works with a trickle-down approach to wealth and ideas, this solution needs to come from the top, not from those at the bottom who are simply told "there's plenty out there who will do this job if you don't like the way it works".