I was talking to my mom about this the other day, and she told me about a woman she knew that once, when asked why she was always 15+ min early to everything, explained that being late was basically disrespecting whomever you're meeting, signalling that their time is less important than yours. So she made sure that she and her family were never late.
Your mom was wise to share this with you, it's an extremely important attribute to have in life. Anyone that says otherwise or thinks otherwise is wrong. It absolutely tells someone that your time is more valuable than theirs. Even if you are a busier person, with more on your plate, you show great composure and thoughtfulness by being on time or early. Also, I consider being "on time" for a reservation at a restaurant the same thing. This is a business that depends on being able to "turn tables" in a timely manor and you are going to be 30 minutes late... fuck you. :) Don't be that guy.