A Question About Kids and Communion

Recently, I've faced a question at church about children and communion.  We had some issues where young kids (about 5 years old) wanted to take part in communion.  The mother talked about how this little one really wanted to take part in communion.

In the Disciples of Christ, kids usually get baptized around age 11 or 12 and usually then participates in communion.  But these days, kids really want to participate sooner and many people think it's important to not exclude kids from communion, even if they have not been baptized yet.

For me, this is an issue that I struggle with.  On the one hand, I hear the  pleading voice of children who want to be included and how could I not?  On the other hand, I grew up (in my Baptist upbringing) learning that one had to wait until baptism to take part in communion.

Historically, people did not have communion until they were baptized usually during Easter vigil. Of course, just because it was done in the past, doesn't mean we should do it today.

So, I want to ask a question: what are the theological reasons for including kids, regardless of age or being baptized, in the Lord's Supper?  Also, was the older way of waiting until a certain age just about people hating children or was there a reason for it?  Has something changed or have we just become more enlightened?

I would lean towards including kids, but I want a reason that's more than "let's be inclusive."  Inclusivity is important, but I want to know why we should do this.