It's the humility of man that admits God is an unreachable mystery for us and that we can at best be compared to His sheep. Last time I checked, cheep don't have a "fellowship" with their shepherd! I think it would be very presumptuous of any sheep to assume that the shepherd is anything more than recognizable but never "known," or, God forbid, "understood."
It is the arrogance of the Reformed that arrogates God to a "personal God" by elevating the status of the "elect" sheep to that of a "fellowship" with the Supreme Being.
I would call that a rejection of the relationship God designed us to have with Him. Of course it is not a relationship among equals, however, it is meaningful and real. As you correctly note, people do not commune (fellowship) with sheep. However, through Christ men DO commune with God:
1 John 1:3 : We proclaim to you what we have seen and heard, so that you also may have fellowship with us. And our fellowship is with the Father and with his Son, Jesus Christ.
1 Cor 2:11-14 : 11 For who among men knows the thoughts of a man except the man's spirit within him? In the same way no one knows the thoughts of God except the Spirit of God. 12 We have not received the spirit of the world but the Spirit who is from God, that we may understand what God has freely given us. 13 This is what we speak, not in words taught us by human wisdom but in words taught by the Spirit, expressing spiritual truths in spiritual words. 14 The man without the Spirit does not accept the things that come from the Spirit of God, for they are foolishness to him, and he cannot understand them, because they are spiritually discerned.
As you can see, there is no comparison between our relationship to animals and ours to God.
It is the arrogance of the Reformed that arrogates God to a "personal God" by elevating the status of the "elect" sheep to that of a "fellowship" with the Supreme Being.
I suppose He will allow you to opt out, but it's your loss. :)