That God is our Father is true in a number of senses. One way in which He is fatherly is that He can simultaneously love us and be angry with us, but the love lasts longer than the anger.
When a child disobeys their parents, their parents do not stop loving the child. Indeed, love is often the very motivation for discipline. But the anger and discipline should never outlast the sin and correction. Rather, it should swiftly die once the behaviour or attitude has been corrected.
With God, the same applies. He disciplines whom He loves, and that discipline is ultimately intended to solve a problematic behaviour or attitude, improving our relationship with Him and conforming us to the image of His Son.