Unforgiveness is the willful choice to refuse to give up negative feelings and the right to get even demanding that someone has to pay for the offense you feel was committed against you or someone else. It is a very serious sin and has some very serious consequences.
"It takes me time to forgive. It will take me a while to get over it. I'll avoid them until then." What this speaker is saying is that they are slow to obey, are not in touch with their own failings and God's redemptive work in their lives, and they will punish them with silence and absence. This is not our example. God doesn't treat us like that. I am thankful for the people who have exampled Him in my life by forgiving me quickly and eagerly.
If they are a godly person who stumbled, they are going to probably forgive you and move on with it. You are the one who will be suffering loss while they are trying to learn and gain all of the spiritual growth out of the situation. You look like a weak Christian, but they are growing stronger in the Lord. Their testimony increases while yours decreases.