He can not be his father!
(Spoilers ahead)
There are two reasonable possibilities but none of them fits the actual plot of this movie:
1. Kyle Reese is an adult man (over 30), living in 2029 and born after nuclear catastrophe. There's no John Connor at that time. Reese goes back to past (1984), has sex with Sarah Connor and eventually dies. Their son grows to be John Connor - leader of resistance movement in 2029,
or
2. Kyle Reese is an adult man, living in 2029 alongside John Connor, leader of resistance movement, who is probably a couple of years older than him, because he was conceived before nuclear catastrophe. Reese goes back to past (1984), has sex with Sarah Connor and eventually dies. By doing so, he messes up big time - John Connor the leader of resistance movement is never born and doesn't exist in 2029. Kyle and Sarah have another baby, but that can't be the John Connor from where Reese started off.