iMessages won't send on my MacBook

Try going through this checklist.

iMessage checklist

iPhone and Mac both logged in to same Apple ID. Try logging off and logging on if necessary.

iPhone Settings => Messages shows iMessage as "on" (sometimes toggling this off and then on fixes some things)

iPhone Settings => Messages shows Send & Receive showing both phone number and email (Apple ID)

iPhone Settings => Messages shows Text Message Forwarding and your Mac is listed and shown as "on" there.

iPhone Settings => Messages shows Send as SMS "on" and MMS Messaging and Group Messaging both "on"

On the Mac: Messages => Preferences shows same and correct Apple ID and "You can be reached for messages at" indicates both phone number and Apple ID (email), and "start new conversations from" indicates the phone number.

* Don't see the Text Message Forwarding setting on your iPhone? Go to Settings > Messages, turn off iMessage, turn it back on, tap Send & Receive, tap Use Your Apple ID for iMessage, then sign in with the same Apple ID used on your other devices.

How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support

The referring article didn't help? If you can’t send or receive messages on your Mac - Apple Support