It’s biblical – while you won’t find the phrase ‘church membership’ in the Bible, the concept is assumed throughout, that every Christian is a member of a local church, that there is no biblical category for a Christian who lives independently from the local church.
The church is made up of members – to be a church is to be one of its members. The church isn’t just the individual Christian, the church is its members (i.e. the body of Christ).
Our obligation to Christ is an obligation to his body – we’re not obligated to the body of Christ only when it’s comfortable, or when it suits us, just as we’re not obligated to Christ only when it’s comfortable, or when it suits us. Instead, our obligation to Christ is also an obligation to his body.
It’s a pre-requisite for the Lord’s Supper – the Lord’s Supper is a meal for the gathered church (1 Cor. 11:20, 33), that is, for its members corporately. The Lord’s Supper is not a private mystical experience with Jesus, but a meal celebrated together with the gathered church.
It’s how to serve other Christians – membership helps you to know which Christians you’re specifically responsible to love, serve, and encourage. It enables you to fulfill your biblical responsibilities to Christ’s body (e.g. Ephesian 4:25-32).
It’s how to submit to Christian elders –membership helps you to know which elders you’re called to submit to, it allows you to fulfill your biblical responsibility to them (Hebrews 13:7, 17)
It helps Christian elders lead – membership lets elders know which Christians they’ll “give an account” for (Acts 20:28, 1 Peter 5:2).
It enables church discipline – it gives you the biblically prescribed place to participate in the work of church discipline responsibly, wisely, and lovingly (Matthew 18:15-35, 1 Corinthians 5)