How will our children know about the statutes, the testimonies, and the means of grace like the Lord's Supper, if they are shuttled off to children's programs for the majority of the worship service? I can think of just a few reasons why babies and children are encouraged to be removed from the service.
1) If we remove them to protect them from some of the topic matter in Scripture and sermons, why do we feel that some Scriptures are unsuitable for children's ears? Why can't we work harder as parents to bring Scriptures down to a level that children can understand, and how can we do that if they're not even with us?
2) If we remove them to protect them from becoming bored, are we not teaching them that the service is boring rather than finding ways to make it applicable and interesting to them? And with babies, would it not be better to strive to teach them to be quiet during the quiet parts as they grow? I understand that babies are noisy - I have one. When Adelaide gets noisy, we get up and stand in the back while bouncing her. This helps her to be quiet, and when she calms down, we sit back down. When she gets older and starts to chatter too much, we will do our best to shush her and, if she still is too noisy for a time, we will take her to the cry room or the foyer where we can still see and hear the service until she is quiet and we can bring her back in. As she gets older and understands better, I think she can learn to hush and entertain herself. Isn't this how parents functioned within the church for centuries? Why all of a sudden do we feel the need to let our children be noisy and avoid boredom at all cost? As they get older, why can't we help them listen to the sermon rather than play with toys and read a book? There are many ways to do this, my favorite being an idea by Edith Schaeffer (Francis Schaeffer's wife). She used to take a sketch book into church with her and her grandchildren and find ways to simply draw the concepts in the sermon for the youngest children. This way, she was using the time to listen, absorb, and teach the children the message in their own visual language. You don't need to be an artist to do this; line drawings work fine. She had simple symbols for Jesus (I think a cross?), God (three dots to represent the Trinity), etc., and once the young children learned this simple system, she was able to help them understand more about the teachings.
3) Do we remove children to protect the congregation (and parents) from distraction? This argument actually makes me the most frustrated because it demonstrates a sad level of individualistic thought rather than thought for the Body as a unit. If people give parents of babies and young children dirty looks when their child coos or quietly fusses for a minute, I feel like they need to closely examine their own hearts about why they are sitting in church. As I said above, has the church not, for centuries, participated in worship amidst some noise? I'm not talking about screaming babies or disorderly conduct, but it is impossible for me to picture the early church meeting in houses or synagogues and not having at least some noise from children or congregants. Why do we now feel that our worship services must be silent, as though we were at a movie theater or a play? We are active participants in worship; must we sit silently observing all that is taking place up front? That seems to be the expectation of some, but I rebel against this idea, and not just in terms of children, but in terms of all of worship. Again, I'm not talking about disorder or chaos, I'm talking about the active participation of young and old in a worship service.
Above all, it brings me great joy to see children sitting with their parents, learning about the Family they have been born into and the Great Father above us all. I love to hear the baby babbling quietly across the aisle and I always have. It gives me a chance to observe godly parents at work and brought me hope when we didn't have our own baby yet. Now, seeing slightly older children in the service from time to time brings me hope again that Lyddie will be with us learning about our Lord and choosing to walk in His ways.