The Apostle John can write generically and specifically within the same sentence (as he often does throughout his gospel and his letters). Here, he writes that God gave his one and only Son. In the context, God is clearly the Father; however, even though we know in the specific sense that God is the Father we shouldn’t ignore the general fact that God has given something. If we solely focus on the Father giving his Son, we can forget that God has given of himself.