No modern president has skipped the next president's inauguration, with the exception of Nixon. It is symbolic of a peaceful turnover. Trump does not care about that. He just cares about himself.
Nations across the globe are taking notes on Trump's actions. We do not have the standing to lecture other countries about fair elections and peaceful turnover of power. We cannot enter into international pacts now because Trump showed the prez can just end them at his whim. They lost their meaning and power.