Children and Communion
When fencing the table, the minister will call on unbelievers to not participate ("lest you eat and drink condemnation upon yourself"). Why do we exclude baptized children of believers, along with unbelievers?
This isn't something I put much thought into until I tried and failed to get any PCA presbytery interested in planting a church in my area, and then looked into the CREC for the same reason. Paedocommunion is one of several distinctives of that [we-are-not-a-denomination-we-are-a-communion-]denomination. In my discussions with them, I was encouraged to learn about these various distinctives. And I did.
It seems like the go-to argument against paedocommunion is 1 Corinthians 11:28 (ESV):
Let a person examine himself, then, and so eat of the bread and drink of the cup.
As always, context is key. The bulk of the chapter is all about people who were basically making a mockery of the sacrament. Some were neglected. Others were over-indulging (to put it mildly).
Concluding that chapter, Paul writes:
So then, my brothers, when you come together to eat, wait for one another— if anyone is hungry, let him eat at home—so that when you come together it will not be for judgment.
If our conclusion from v28 is that "examine himself" means being aware of our generally sinful estate (which is the mainstream understanding) vs being aware of what the writer actually says:
But in the following instructions I do not commend you....
...then that's a not insignificant leap away from the obvious context to a conclusion that doesn't seem to be stated in the least. This is the constant danger of one-off “proof verse” hermeneutics. There’s probably a verse or a sentence somewhere to “prove” whatever you want to prove as long as you’re not worried about the whole “context thing.”
On the flip side of this are all of the scriptural examples that form Covenant Theology, wherein little distinction is made between a believing man and that of his family. Except when it comes to communion, apparently.
Of course, if your church entirely disenfranchises its children, then this topic is neither here nor there.