I have to say that is not my experience. Most couples I know who have children wanted them equally. In some cases, the man wanted them before the woman did. And it took her 2-3 years to catch up.
My brother, my DH, my DH's brother, my 2 BFF's husbands, my 2 male cousins to name but a few wanted children before their wife did. (Or at the same time roughly...) The men were ecstatic when they discovered they were going to be a dad! I couldn't stop DH grinning when I told him the news. It was like he had a coathanger in his mouth! He was over the moon.
Several couples I know split up because he wanted a child and she didn't.
It's a myth that 'men only have children because the wife wants them.' This may be true in some cases, but certainly not all. I think this is a thing that some child free women want to believe, and some child free men.... (Not all of course.)
Not sure why married men are going around telling random childfree women that they didn't want children and only had them because the missus wanted them. Why on earth are 'many men' telling you this? 
It's OK to be child free. No need to try and point score by claiming 'men don't want them, it's only women who do' because that's simply not true. Not in all cases.
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