When dealing with people, loyalty can sometimes be a virtue. This is because people are inherently unpredictable but yet deterministic (future actions are somewhat based on past actions); you'd expect a person to behave in mostly the same way that is supposedly in line with your personal interests. Hanging around (being loyal) with "the right people" is then a move that would probably lead to future benefit.
When dealing with objects, loyalty is a useless but mostly harmless attribute. Hanging on to "my trusty pen" is completely irrational, but usually doesn't pose a significant downside.
I liken the non-materialistic upgrading of tools to be the best display of loyalty for utility's sake. For the graphic designer, this could be upgrading to a new, more powerful laptop which has the processing power to serve their intensive vector manipulation needs. They pack up their old laptop, kiss it goodbye (trash or resale), and say, "Thank You! You Served Me Well!"
The dangerous bit comes when dealing with ideas.
There's a tendency to associate one's ideas with oneself. This leads to an inner conflict once those ideas are challenged. Do I defend? Do I attack back? Was I really wrong? No, here's the truth! etc....
We see this with religion, where loyalty to people (pastor, fellow congregation) evolves into loyalty to objects (the symbols), which then evolves to loyalty to identity (oneself). At that stage, religion loses its virtue. The same goes for the battles between opposing schools of thought. Whether they be in dance or in statistics, the underlying battle is one between egos.
As Paul Graham as mentioned, it pays to keep your identity small. In line with that principle, it's important to be able to quickly dismiss an idea that has outlived its utility with a simple phrase:
"Thank You! You Served Me Well!"