The illustration of the two brides that
@PeteR has pointed out is completely true. However, simultaneously, there are other informative ways to look at this.
The word "Ekklesia" / "assembly" / "church" is a plural word. It does not refer to a single individual, but to a large number of individuals. It isn't a singular bride, but a collection of "brides".
We are told that just as a wife is "one flesh" with her husband, each of us is "one spirit" with Christ. In other words, the relationship each of us has, individually, to Him, parallels marriage. We are each individually married to Him, not just as a collective.
So the church can be also looked at as "the holy harem of God", rather than a singular bride.
And this makes far more sense than the church being a singular bride. It is our job to go out and evangelise, to bring more people into the harem. And it doesn't matter how many more people join the bride / church / harem, each of us still has our same one-spirit relationship with Him that is not diminished in any way by the fact that we are "sharing" HIm. This perfectly parallels earthly marriage.
Also, the monogamous singular bride concept is an opening for cults to say "we are the only bride of Christ, and you have to be in this church to be in the bride".
The other very important thing to remember is that the concept that the church is the monogamous Bride of Christ is not actually in the Bible. It was developed later in Catholic theology. The only entity described as something like the Bride of Christ, in the New Testament, is actually the city of New Jerusalem. But the concept that each of us has a one-spirit relationship with Christ, paralleling earthly marriage, is very scriptural - as is the two houses being two brides. So the only illustrations of the church as a "bride", in scripture, are polygamous and not monogamous!