If emails are moving directly to Archive folder or All mail folder (Gmail account) there can be following reason behind this:

  • Particular contact is added in Blocked list

Go to Airmail preferences > Favorites > Blocked list > enable and the list will appear in the side bar with other folders.
Please check if the contact is appearing under the Blocked list in side bar, if so, Control click the contact > Delete from Blocked list

  • It may be a rule in Airmail or Filter on Server side to archive the emails automatically. 

You can check the rules in Airmail from Window menu > Rules

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