I do not agree with their position, but I do understand where they are coming from. These are usually people who not only believe in biblical inerrancy, but also believe that the correct interpretation of any passage of Scripture is that which is dictated by the plain meaning of the words. Generally, this means that, while they have some appreciation of written context, historical and social context is generally disregarded by those with this particular theological leaning.
The viewpoint that you describe comes from a particualrly literalist reading of Genesis 9:7 (and similar passages). From this, they conclude that we have a moral obligation to have as many children as possible, so as to ensure that the earth remains as heavily populated as possible. Given their interpretative methodology, this is an entirely reasonable understanding of this passage. However, I believe that this interpretaion becomes questionable when considered in the light of historical and social context.