Traditionally, people threw rice at weddings. I don't know how old this tradition was, but numerous internet sources suggest that it dates to ancient times in some form or another, and that the use of rice reflected guests' wishes that the newlywed couple have a lifetime of fruitfulness and prosperity. This makes a lot of sense.
Though not actually providing the couple with a meal, literally showering them with food is powerfully symbolic. (I'm reminded of It's a Wonderful Life, when Mary Bailey hands the Martinis "bread, that this house may never know hunger; salt, that life may always have flavor; and wine, that joy and prosperity may reign forever.")
We're not allowed to throw rice after our wedding. Though the exploding-bird thing appears to be a myth, there are apparently worries about both liability (someone might slip) and clean-up (someone's gotta clean it up). I might, I suppose, accept a substitute of birdseed, confetti, rose petals, etc. Throwing something just feels, viscerally, to be connected to the age-old practice of throwing rice. Like it means something. Those, however, offer the same disadvantages to the church, and are similarly forbidden. (I wanted to invent something that could be thrown at newlyweds that would not cause a mess or a safety hazard, but it's kind of hard to do.)
What could we do instead? Most people blow bubbles these days. Some ring bells. And honestly, I'm not feelin' it. Bubbles have been blown at every wedding I remember being at (I think I might have gotten to throw rice once, as a little girl, before it was forbidden, but I can't remember clearly), and I never had any objection. They were fun and they were pretty. What's not to like? But I'm trying to be a little more mindful in planning my wedding than I ever was as a guest. I had never asked myself "Why blow bubbles?" before, but I'm asking it now, and, as best I can tell, there's no answer. If I had asked, "Why throw rice?" I would have gotten an answer. I wouldn't have staked my life on its historicity, but I could have more or less believed that people were throwing rice at us because they wanted us to have a fruitful and prosperous life. But I can't come up with an answer for "Why blow bubbles?" Instead of blowing bubbles without knowing why - replacing powerful symbolism with empty show - I think we're going to skip it.