The words man and woman refers to gender, where as male and female refer to sex.
Man is somebody who regardless to what they were born physically has masculine traits, and identifies as such. It's how the mind thinks, and functions.
Woman is somebody who regardless to what they were born physically has feminine traits, and identifies as such. Again, it's how the mind thinks, and functions.
Male is somebody who has male genitalia, produces much more testosterone over estrogen, and typically has a more triangular body structure. This is the body physically.
Female is somebody who has female genitalia, produces much more estrogen over testosterone, and typically has a more hour glass body structure. This is the body physically.
He is a man because he identifies as a man. If it were not for his being pregnant publicly you would never have thought of him to be female, or a woman in any way shape or form.
His wife is unable to physically give birth, so he's using what he has in order to start a family. The entire adoption process is completely, and totally messed up so I can understand why they might not want to go that route. That, and it costs much more than any sort of fertilization would.
There is a documentary called Transparent about FtM (female to male) people who have given birth. They either were on hormones then had children, or started hormones after giving birth. It's a wonderful film, and gives insight by MANY people that have gone through it instead of just one person.
Some in the film are homosexual men who were impregnated by their boyfriends/fiance/partners.