Respecting your time and the time of others is a good attribute to have. When you are late, it signals to the other person that you do not respect their time. Most people are not that pleased with this signal. Although a few people will be happy when you are running late. This is especially true when they are running late themselves.
Showing up early demonstrates you are in control of your time. It allows you time to park, register or prepare. It also signals that you are mature and respectful of the time of others.
This characteristic can buy a lot of goodwill. It is a good one to have. Certainly it is one to work on if you are not demonstrating it consistently.
No need to make a reason or excuse. The evidence is there. Best not to make it a habit. Exceptional circumstances only, outside of your control, is a good rule to live by. Communicate the timing expectations as soon as adversity is encountered. This can also ease the tension at the other end.
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