This father is talking about a young child. At that age, biological girls tend to physically mature faster than biological boys. Without knowing the specifics about his child, it is problematic to claim his child will somehow have a biological advantage over others.
As to the infringement of rights of the other children argument, it works in both directions. The champions of the biological girls' rights have no problem infringing on the rights of the transgender children. Any outcome between competing interests in the law has to infringe on the perceived rights of someone.
Prior to puberty, there's not a material difference between males and females. One puberty begins, however, the difference is significant.
As far as the idea that females being allowed to compete against other females with the same biological competencies and barriers is somehow an infringement on the right of males to compete against females... I don't really know what to say to that. Transgender children already have the right to compete against others of their same sex. What's being asked for is not equal rights, but special rights - the right to compete against people with a clear physical disadvantage, and to displace females in sports. What is the reason? It's not so that transgirls have a "fair shot" - they're biologically male and already have a fair shot against other males. They have an unfair shot against females. The overriding argument for why transgirls should be allowed to compete against females is to affirm their feelings, to make them feel good about themselves. The fact that this hurts the feelings of female athletes, the fact that this makes females feel displaced and bad... that's of no account.
The feelings of males are more important than the feelings of females. In many cases, the feelings of males are treated as more important than the rights, safety, and dignity of females.