The statement isn’t entirely false. We all should be united. And in some sense, all Christians that have been baptized are. It’s just that, unfortunately, full unity doesn’t exist right now.
The problem with the “no denominations” stance is that unity of this nature requires agreement. Take baptism for example. Catholics, Lutherans, and Presbyterians, among others, baptize infants. Baptists, Nazarenes, and Assembly of God, among others, don’t. Further, those denominations that baptize infants tend to be very much against re-baptism, whereas those who are against infant baptism tend to be very much for the re-baptism of those who were baptized as infants. (I actually remember once a Baptist pastor (I think John Piper) told a Presbyterian one (I think Tim Keller) that many people at that Presbyterian pastor’s church wouldn’t be able to receive communion in the Baptist church since they were, by Baptist standards, not baptized.) Obviously, that will cause dilemmas, especially if either side as reasonable convictions as they seek to prevent others from disobeying God (whether or not they actually are).
Also consider Communion. Catholics believe in transubstantiation and that no one should receive unless they also believe it, and we shouldn’t take of Communion at other churches where they don’t believe it. Further, we believe the Eucharist is the “source and summit of the Christian life”, so permanently abstaining doesn’t make sense. However, all Protestant groups to my knowledge reject transubstantiation. Again, we have a serious dilemma.
Also consider the administration of the sacraments. Catholics and Presbyterians, among others, believe that it must be done by an ordained minister. Baptists might be far more lenient and may not even believe in sacraments. Further, among those who believe the person must be ordained, the requirements of that ordination is different. Since Presbyterian ministers didn’t receive authority from a valid bishop, we wouldn’t recognize their authority. Again, we have a dilemma.
And don’t even get me started on apostolic succession and the Pope!
I could go on and on, but the basic summary is that the “no denomination” only works if we either all agree to the extent that none are seen as in disobedience and/or heresy or we water down Christianity to the point that it is practically meaningless. Notably, I don’t think I’ve ever met a non-denominational who wasn’t Baptist or Pentecostal at their core. Sure, they still water down the faith quite a bit, but they’d also probably be put off by some of the beliefs and practices of Catholics, Orthodox, Lutherans, Presbyterians, and Anglicans.
So while there is some truth in the sentiment that there shouldn’t be all this division, achieving that through non-denominationalism is a pipe dream.