Dave Armstrong at Patheos Catholic has pointed out that early Protestants "detested divisions" and were very concerned to maintain unity.
He's right. The most basic argument against Protestantism, which does not require any particular theological premises about authority, is
1. The Protestants expected and claimed that all Christians of good will ("endowed with the Spirit" as my dissertation subject Martin Bucer would put it) would be able to see that their interpretation of Scripture was correct, and that by unleashing Scripture a renewed and reunified Church would emerge. (It's important to bear in mind that early sixteenth-century Christians saw the Church as divided and fractious, and were looking for _greater_ unity, not less).
2. This didn't happen.
3. Therefore, by the standards of the early Reformers themselves, Protestantism is a failure.
Instead of admitting this, Protestants have spent 500 years arguing either that [visible] unity really doesn't matter or that it will happen if we only get one more bit of light out of Scripture or throw off one more unbiblical tradition.
Of course this is painting with a huge brush. Many Protestants do recognize this. But as a whole, Protestantism tends to take the Reformers as a model either substantively (by trying to follow their doctrines) or methodologically ("ecclesia semper reformanda"/"God hath yet more light to break forth out of His Holy Word") or both. And both of these approaches have proven disastrous.