Why betrothal?

Short answer : Because this is the relationship between Christ and His bride, and because human marriages are explicitly intended by God to reflect Christ's marriage.

Christ has made an irrevocable commitment to His bride, and His bride is irrevocably promised to Him in marriage. The wedding feast has not yet taken place. The marriage is not yet consummated. Christ waits patiently and eagerly for the day He comes to claim His bride.

Right now, Christ is in Heaven, preparing a place for His bride.

He can return at any time.

He will return.

This is the explicit Scriptural teaching of the relationship between Christ and His bride (the Church). It also exactly fits the Scriptural clues as to the definition of betrothal.

Caveat : Does this mean that any Christian who chooses engagement instead of betrothal is sinning? No. But does it mean that Christians who wish to honour the Lord in this way can do so by way of an irrevocable engagement, also known as a betrothal? Yes.