If it’s true that animals have high status according to Christian doctrine—I must say, such a thing seems to have gone unnoticed by scholars during all the two thousand years of Christian tradition.
If this is incorrect, please let me know.
The animals were created just below man, and man was given dominion over them. I agree, man has not always done this (or anything else, for that matter) all that well, but that is created order before sin. The sacrifice of Jesus offers us the opportunity - as followers of Jesus - to be restored to that created order and to be at one with Him. The animals are not offered (nor do they need) this gift of grace.
It would depend on what you mean by “high status”. Many Christian thinkers and apologists have preached on the issue of animals having an after-life. There is much Biblical evidence to support this, and it’s only been in recent times that mankind has treated this as some type of “threat” to his own “special relationship” to the Lord. More indicative of the mentality of humanity than of God having changed His mind about animals being eternal (remember the Garden?) God loves all of His creation far more than humanity is capable of understanding — and not just His two-legged creation, either. He cared enough for animals to insist that they be given a rest on the 7th day - as their owners were to do for themselves, and He made a covenant with them after the Flood — as He did with Noah. Animals are only at the bottom of the totem pole for some who haven’t bothered to read their Scriptures. (And the concept of worshiping the creation applies just as well to the worship of children and idolatry that some parents exhibit on their behalf.... Just sayin’.)