There are times when tenacity, that is the ability to firmly grip something and not let it go, is admirable.  Also, there are times when letting go is the better option.

The balance between determinedly following a course of action (e.g. a personal career path) and changing direction (taking a new career path) is not always an easy one to follow.

Just Move On

Holding on relentlessly can cause internal anxiety for you but can also color other peoples perspectives of you in a negative way.  Being perceived as the stubborn or intractable is a negative spin, it is better to be seen as firm or tenacious.

Managing how others view you is an important life skill.  Recognizing when to drop something is a key part of this.  That does not necessarily mean acquiescence, but rather closing a topic in a way acceptable to everyone that is involved.

Often, to do this, you need to be able to recognize when it makes sense to just let it go.  When arguing or ongoing discussion is clearly just fostering continued disagreement it is likely time to shut it down.

Not Giving Up

It is important to distinguish between letting go and giving up.  These are very different approaches, albeit they can appear to have the same outcome.

Giving up will lead to personal baggage and potentially you will feel bad about yourself.  Letting go is about recognizing that hanging on is painful to you and getting nowhere.

Releasing the pent up emotion which is eating away at you for something that is unlikely to change can be resolved simply by accepting the way it is and moving on.