Looking from a mans point of view,if you meet and fall in love with a woman

plus take on the responsibility of children of a previous union.

Provide for them, love them as your own for an extended period of time,

to then be told years down the track when a problem arises that

"My children will always come first"

Is a pretty big slap in the face to any guy, don't you agree 

Well, I agree with you even if lind9650 doesn't.

I understand the social dynamics of having children and about the evolutionary pressures which drive a woman's imperative to care for her children above all others.

The ancient biological/evolutionary drives cause a man to care about his children (and his woman) until the kids reach an age where they can survive without him.

Then he leaves to find another woman who can give him more children. and repeat the same pattern.

This is a sort of intuitive behavior, a behavior which is purely on the animalistic, survival-of-the-species level.

Our current constructs surrounding the relationships between the sexes and between the children of such relationships are a result of an increased degree of civilisation where the effort to just survive is no longer so much at the fore-front of our (species') consideration.

We're a lot more sophisticated nowadays than our primitive forebears were and we now experience a situation where a man might invest his time and effort and his finances in the support of children who are not his own because he values the companionship and the love of a good woman more than he values his wealth (such as it is).

and then he is told "My children and their needs will always take precedence over you and your needs."

and then he thinks to himself "why did I even bother?"

I think that the reason we have children at all is a selfish reason. (there's a biological and evolutionary selfishness where we are driven to breed, just like other animals) and there's a social reason to have kids as well which may vary according to the culture and society one lives in.

 There's no modern moral imperative to breed; in fact, the moral position would be to have a minimal number of children. (in some cultures there might be a religious imperative to create more little faithful god-botherers)

If women want a good and faithful man then they have to be good and faithful themselves (social contract).

If a woman tells her man that her children (from a prior relationship) will always take precedence over him, then she's really expecting a lot to expect from him his undivided loyalty, love and (financial as well as emotional) support.

Children are sometimes seen as being some sort of sacred object.

The whole world is seething and crawling with millions upon millions of these little voracious consumers who, let's face it, consider their own interests first; that's evolutionary elementary.

Are we, even after all these many hundreds of thousands of years of human development, still hung up on the evolutionary and biological imperatives which dictate our attitudes to and our desire for children?

Yep, we're still animals, after all, even if we now have the capacity to think about and to reflect on what motive forces drive our behavior.

(well, some of us think and reflect about this sort of stuff . . . . others just unthinkingly churn out children as if this were a normal way to live, despite the fact that our planet is dying because of pressure of the numbers of its human population)

On Children
 Kahlil Gibran

Your children are not your children.
They are the sons and daughters of Life's longing for itself.
They come through you but not from you,
And though they are with you yet they belong not to you.

You may give them your love but not your thoughts,
For they have their own thoughts.
You may house their bodies but not their souls,
For their souls dwell in the house of tomorrow,
which you cannot visit, not even in your dreams.
You may strive to be like them,
but seek not to make them like you.
For life goes not backward nor tarries with yesterday.

You are the bows from which your children
as living arrows are sent forth.
The archer sees the mark upon the path of the infinite,
and He bends you with His might
that His arrows may go swift and far.
Let your bending in the archer's hand be for gladness;
For even as He loves the arrow that flies,
so He loves also the bow that is stable.

Of-course, child has to be always the first priority for people of all genders.  The child is totally dependent on its parents, and when there is a conflict of interest between the child and partner, the child has to come 1st.  As child grows and its dependence on parents is slowly diminishing than the balance is changing.  Partners need to understand that, be they biological partners or not.  That does not go just for men.  Some years ago I was in relationship with a man who had 2 teenage children, while my own daughter was grown up and totally independent.  His kids were 12 and 14 when I first met him, and in the age needing lots of support and understanding, and it would never for a second occur to me that I should have precedence over them.  by the way, I was the wealthier one in that relationship.

I suspect that the people who are saying that woman should put her partner before her children, are the same people who would say she is a bad mother if she did that.