This obviously is not the angel being offended at Zacharias’ mistrust of his words in a personal way. That sort of response only comes from pride and the holy angels are void of pride.
Unbelief always results in loss. God wants us to respond to all his says with faith, and his word warrants faith no matter how great the promise. We must always remember who it is who is speaking. He says nothing that ever raises false hope, false expectation. We cannot exercise more faith than is warranted when we hear the promises of God. Faith can go out on a limb and expect to have its weight borne. How much better it would have been for Zacharias to believe what he was told! He would then have triumphed over his difficulties and walked hand in hand with the promise until it was realised.