• The Laws of Logic Hold Universally
• Christianity's distinctive, characteristic beliefs

• the Father is characteristically angry and wrathful
• the Son is characteristically merciful and loving
• If the above is true, the Father and Son are characteristically different

∴ the Father and Son are characteristically different

Marcion

x the Father and Son are characteristically different

There is another line of reasoning that says the Father can have multiple emotions fundamentally characterize Him (for His emotive abilities are far beyond our own). So, this would potentially be a logical response based on the idea that God can somewhat step outside our conceptions of logic.

Another logical response would involve simply saying that multiple kinds of emotions can characterize someone.