~~Christ does~~ Christians do say canonically that the church is like Christ's wife.
Marriage—Christ and the Church
22 Wives, submit to your own husbands, as to the Lord. 23 For the husband is head of the wife, as also Christ is head of the church; and He is the Savior of the body. 24 Therefore, just as the church is subject to Christ, so let the wives be to their own husbands in everything.
(Ephesians 5:22-24)
And bridal theology goes back to the Old Testament, in Song of Songs.
Thanks for pointing out that it was Paul not Jesus who said that. I feel silly now. Corrected my comment.