One reason your uncle finds it hard to apologize could be embarrassment; it's just easier for him to pretend nothing happened than to face the embarrassment of admitting he was wrong. You've probably done the same thing yourself at some time; most of us have.
But a deeper reason is pride. Pride blinds us to our sins (or at least it makes us downplay its seriousness). Pride also makes us unwilling to admit to others that we were wrong. Perhaps we're afraid they'll look down on us if we do admit it; we may even hope that somehow they will overlook it.
But others see through our pride, and (as you suggest) things would be far better if we admitted our faults and asked for forgiveness from those we have hurt. Otherwise our pride will only hurt us and cause conflict with others. The Bible warns, "The eyes of the arrogant man will be humbled and the pride of men brought low" (Isaiah 2:11).
Pray for your uncle–not only that he'll learn how to apologize and ask for forgiveness from others, but that he'll face his need for God's forgiveness and open his heart to Christ. We have offended God even more than we have offended others–but God still loves us, and Christ came to forgive us. Have you turned to Him for the forgiveness and new life you need?