You seem to be confused: the author states "The truth is that I don’t cry because I miss them [...]" and then you go "[...] never once did I feel like crying because I missed them. I did miss them, just not to the point of breaking down into tears:)"

In any case it is likely the author's relations to his family and your relations to your family are different and as such you feel differently when separated. It is also likely the circumstances are different.