Avast is trying to act as a proxy i.e. middleman between your email client and email server. You most likely have to configure your accounts in avast so it knows to act as the middleman for them.
RealTimeShields>MailShield>Expert settings>SSL accounts
You will need to add entries for each account - most likely two rules: one for inbound 9POP3) and one for outbound (SMTP). Check your email client configuration first so you have all the right protocol/port information. Once this is set up you will have disable SSL in your mail client but your server should still be happy since avast is sending SSL traffic to it.
As per the help documentaiton:
On this screen you can enter details of how your Mail Clients communicate with the Mail Server, including, where encryption is required, the type of encryption that is used.
In order for mail to be scanned by the Mail Shield, it is necessary that encryption is turned off in your Mail Client.
If encryption is required, the information on this screen will then be used to establish a secure connection between the Mail Shield and the Mail Server. This will enable all incoming and outgoing mail to be scanned by the Mail Shield. Unencrypted connections do not need to be listed.
The outgoing unencrypted email will first be scanned by the Mail Shield. If the type of encryption is specified on this page, a secure connection will be established and the mail will be sent encrypted to the Mail Server (if the type of encryption has been specified as "None", the mail will be sent unencrypted). If nothing is specified on this page for a particular mail account, the Mail Shield will check whether the Mail Server supports encryption. If it does, a new rule will be created automatically and the mail will be encrypted and sent to the Mail Server.
As the secure connection is established between the Mail Shield and the Mail Server, incoming mail can be unencrypted when it is received by the Mail Shield and scanned before it is delivered to the Mail Client.
If encryption is not turned off in the Mail Client, the Mail Shield will be unable to scan the content of either incoming or outgoing mail. This means that although the connection will be secure, the mail cannot be scanned by avast! and is therefore unprotected. In this case a warning message will be displayed (by default) informing you that a message has been received via an unprotected SSL connection.
If you do not want to receive this warning, uncheck the box at the bottom of page "Automatically detect and warn about unprotected SSL connection".