Why do some text messages sent to my phone show up on my Mac Air and some texts sent to my phone do not show up on my Mac Air?

Hello!

First, check that iCloud for Messages is enabled. This will sync your iMessage conversations across all your Apple devices that support Messages: Set up iCloud for Messages on all your devices - Apple Support.

Next, check that you're forwarding SMS/MMS text messages from your iPhone to your Mac. With Text Message Forwarding, the SMS/MMS messages that you send and receive on your iPhone can appear on your Mac or iPad as well. Then you can continue the conversation from the device you want: Forward SMS/MMS text messages from your iPhone to your Mac or iPad - Apple Support.

I hope this helps!

-Jack